{:highlights [{:id #uuid "6a787abc-f31a-487e-9c0e-451308dc7e36", :page 2, :position {:bounding {:x1 110.05858866870403, :y1 71.3758544921875, :x2 459.86326090991497, :y2 85.26473999023438, :width 718, :height 1015.4567293154772}, :rects ({:x1 110.05858866870403, :y1 71.3758544921875, :x2 459.86326090991497, :y2 85.26473999023438, :width 718, :height 1015.4567293154772}), :page 2}, :content {:text "두 벡터 가 직교한다는 것은 두 벡터 의 내적 이 0임을 의미한다 ."}, :properties {:color "yellow"}} {:id #uuid "6a787ac1-8770-4b41-a862-8b8ae853cc50", :page 2, :position {:bounding {:x1 479.9696146696806, :y1 71.3758544921875, :x2 585.8723551481962, :y2 85.26473999023438, :width 718, :height 1015.4567293154772}, :rects ({:x1 479.9696146696806, :y1 71.3758544921875, :x2 585.8723551481962, :y2 85.26473999023438, :width 718, :height 1015.4567293154772}), :page 2}, :content {:text " •w=w= 0"}, :properties {:color "yellow"}} {:id #uuid "6a787bd5-b422-4b1e-8203-99d9c164a3ce", :page 2, :position {:bounding {:x1 345.12803141772747, :y1 535.232177734375, :x2 631.9661051481962, :y2 549.1210327148438, :width 718, :height 1015.4567293154772}, :rects ({:x1 345.12803141772747, :y1 535.232177734375, :x2 631.9661051481962, :y2 549.1210327148438, :width 718, :height 1015.4567293154772}), :page 2}, :content {:text "4가지 기본 부분공간 은 서로 직교하는 관계이다 "}, :properties {:color "yellow"}} {:id #uuid "6a787c0d-a229-4698-95fc-bdb87ebf798a", :page 2, :position {:bounding {:x1 103, :y1 562.5555419921875, :x2 659, :y2 650.5555419921875, :width 718, :height 1015.4567293154772}, :rects (), :page 2}, :content {:text "[:span]", :image 1786280971515}, :properties {:color "yellow"}} {:id #uuid "6a787d5d-e3a3-4fd6-bc60-23b45bd56f24", :page 2, :position {:bounding {:x1 112.0008646696806, :y1 671.2456321716309, :x2 656.52952067554, :y2 711.8381004333496, :width 718, :height 1015.4567293154772}, :rects ({:x1 112.0008646696806, :y1 671.2456321716309, :x2 656.52952067554, :y2 685.8289451599121, :width 718, :height 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291.01520793139935, :y2 182.6497344970703, :width 718, :height 1015.4567293154772}), :page 4}, :content {:text "직선 위의 모든 벡터와 평면 위에 모든 벡터 가 서로 직교 하면, 그 직선( 1 차원 부분 공간)과 평면 ( 2차원 부분 공간 ) 은 서로 직교 한다."}, :properties {:color "yellow"}} {:id #uuid "6a787eb2-c989-4164-beca-de440e0edb91", :page 4, :position {:bounding {:x1 183.8758646696806, :y1 244.63975524902344, :x2 440.86997477710247, :y2 257.8341827392578, :width 718, :height 1015.4567293154772}, :rects ({:x1 183.8758646696806, :y1 244.63975524902344, :x2 440.86997477710247, :y2 257.8341827392578, :width 718, :height 1015.4567293154772}), :page 4}, :content {:text "행렬 A의 영공간 은 A의 행공간 과 직교 한다."}, :properties {:color "yellow"}} {:id #uuid "6a787ef7-1822-46e0-8709-ed5e9eb05a05", :page 4, :position {:bounding {:x1 107.4110209196806, :y1 746.8641204833984, :x2 654.1666666716337, :y2 792.3719329833984, :width 718, :height 1015.4567293154772}, :rects ({:x1 532.2916666716337, :y1 746.8641204833984, :x2 654.1666666716337, :y2 763.5308074951172, :width 718, :height 1015.4567293154772} {:x1 107.4110209196806, :y1 776.3997039794922, :x2 323.44834391772747, :y2 792.3719329833984, :width 718, :height 1015.4567293154772}), :page 4}, :content {:text " 의 열공간 C( A) 와 AT 의 영공간 N (AT ) 가 직교한다 "}, :properties {:color "yellow"}} {:id #uuid "6a787f09-1ca3-4fa6-93e5-3e342dc05a83", :page 5, :position {:bounding {:x1 80, :y1 366.027587890625, :x2 602, :y2 410.027587890625, :width 718, :height 1015.4567293154772}, :rects (), :page 5}, :content {:text "[:span]", :image 1786281737047}, :properties {:color "yellow"}} {:id #uuid "6a788137-090c-4660-8c0e-093b7751a47c", :page 5, :position {:bounding {:x1 70.713976547122, :y1 555.0238189697266, :x2 530.2200113981962, :y2 568.9127349853516, :width 718, :height 1015.4567293154772}, :rects ({:x1 70.713976547122, :y1 555.0238189697266, :x2 530.2200113981962, :y2 568.9127349853516, :width 718, :height 1015.4567293154772}), :page 5}, :content {:text "전체 공간 을 구성하는 직교하는 두 부분 공간의 쌍을 특별히 직교여 공간이라 한다"}, :properties {:color "yellow"}} {:id #uuid "6a788141-72f8-496c-b763-902b6938ff79", :page 5, :position {:bounding {:x1 69.7157084196806, :y1 555.0238590240479, :x2 623.4817301481962, :y2 597.8624210357666, :width 718, :height 1015.4567293154772}, :rects ({:x1 541.0698649138212, :y1 555.0238590240479, :x2 623.4817301481962, :y2 568.9127140045166, :width 718, :height 1015.4567293154772} {:x1 69.7157084196806, :y1 584.6679630279541, :x2 342.6239420622587, :y2 597.8624210357666, :width 718, :height 1015.4567293154772}), :page 5}, :content {:text "V의 직교 여공간 V- 은V 와 직교 하는 모든 벡터 를 포함 한다."}, :properties {:color "yellow"}} {:id #uuid "6a788158-f254-4ace-8d7b-92efbb1a5894", :page 5, :position {:bounding {:x1 64, :y1 836.6943359375, :x2 539, :y2 924.6943359375, :width 718, :height 1015.4567293154772}, :rects (), :page 5}, :content {:text "[:span]", :image 1786282327912}, :properties {:color "yellow"}} {:id #uuid "6a7881ad-9b11-4a79-88c1-01464b139f02", :page 7, :position {:bounding {:x1 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{:bounding {:x1 135.54686991870403, :y1 848.2638549804688, :x2 587.887186691165, :y2 861.4583129882812, :width 718, :height 1015.4567293154772}, :rects ({:x1 135.54686991870403, :y1 848.2638549804688, :x2 587.887186691165, :y2 861.4583129882812, :width 718, :height 1015.4567293154772}), :page 7}, :content {:text "해 의 유일성은 해 가 존재 함을 의미 하고, 해 의 존재성은 해가 유일 함을 의미 한다"}, :properties {:color "yellow"}} {:id #uuid "6a788859-b8b0-4ccf-a774-177555adbcec", :page 6, :position {:bounding {:x1 110.41665904223919, :y1 750.2061614990234, :x2 655.13791911304, :y2 792.0138397216797, :width 718, :height 1015.4567293154772}, :rects ({:x1 597.58030192554, :y1 750.2061614990234, :x2 655.13791911304, :y2 763.4005584716797, :width 718, :height 1015.4567293154772} {:x1 110.41665904223919, :y1 778.1249847412109, :x2 326.82050578296185, :y2 792.0138397216797, :width 718, :height 1015.4567293154772}), :page 6}, :content {:text "행렬 A는행공간 에서 열 공간 으로 의 가역변환이다"}, :properties {:color "yellow"}} {:id #uuid "6a788882-d504-47fd-809d-fa131414360a", :page 8, :position {:bounding {:x1 112.85806529223919, :y1 160.90493774414062, :x2 659.4292399138212, :y2 205.14321899414062, :width 718, :height 1015.4567293154772}, :rects ({:x1 112.85806529223919, :y1 160.90493774414062, :x2 659.4292399138212, :y2 176.87716674804688, :width 718, :height 1015.4567293154772} {:x1 112.85806529223919, :y1 191.25436401367188, :x2 453.74433390796185, :y2 205.14321899414062, :width 718, :height 1015.4567293154772}), :page 8}, :content {:text "행 공간의 기저벡터 개와 영공간 의 기저벡터 ( 2-1)개 를 더하면 + ( nr ) = \"개의 벡터가 된다 . 이 \" 개의 벡터는 선형독립 이다 . 따라서 R \"을 생성한다"}, :properties {:color "yellow"}} {:id #uuid "6a7888b9-0f6a-494b-a9e7-3cf7dbe5dd91", :page 4, :position {:bounding {:x1 112.43489329516888, :y1 537.5650863647461, :x2 620.1280314177275, :y2 554.9912948608398, :width 718, :height 1015.4567293154772}, :rects ({:x1 428.91709391772747, :y1 537.5650863647461, :x2 620.1280314177275, :y2 553.5373153686523, :width 718, :height 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"}, :properties {:color "yellow"}} {:id #uuid "6a7a0403-2799-49a5-952d-9fdf5d50e671", :page 13, :position {:bounding {:x1 73.51345317065716, :y1 497.3741226196289, :x2 622.670878097415, :y2 567.3393936157227, :width 718, :height 1015.4567293154772}, :rects ({:x1 464.0299174040556, :y1 497.3741226196289, :x2 622.670878097415, :y2 510.5685501098633, :width 718, :height 1015.4567293154772} {:x1 73.51345317065716, :y1 522.8515396118164, :x2 617.382792159915, :y2 539.518196105957, :width 718, :height 1015.4567293154772} {:x1 73.51345317065716, :y1 551.3671646118164, :x2 261.3311869353056, :y2 567.3393936157227, :width 718, :height 1015.4567293154772}), :page 13}, :content {:text "행렬 A 가 선형독립 인 열을갖는다면, 벡터 b 의 C ( A) 위로의 사영 은 P=A( ATA) 'ATb이다 . 여기서 사영 행렬 P= A( ATA) ' AT는 대칭 행렬이다"}, :properties {:color "yellow"}} {:id #uuid "6a7a040f-bcd4-4e55-863a-6152ed91aa7f", :page 13, :position {:bounding {:x1 72.51518504321575, :y1 551.3671646118164, :x2 619.94358317554, :y2 595.1605606079102, :width 718, :height 1015.4567293154772}, :rects ({:x1 430.3602396696806, :y1 551.3671646118164, :x2 619.94358317554, :y2 567.3393936157227, :width 718, :height 1015.4567293154772} {:x1 72.51518504321575, :y1 579.1883316040039, :x2 332.7189127653837, :y2 595.1605606079102, :width 718, :height 1015.4567293154772}), :page 13}, :content {:text "P2P이다. 즉 두 번째 사영 은 pp로 사영하므로 아무것도 변하지 않는다"}, :properties {:color "yellow"}} {:id #uuid "6a7a0415-779e-42a1-9b91-95340aa2264b", :page 13, :position {:bounding {:x1 87.36979167163372, :y1 741.3844985961914, :x2 616.7273356169462, :y2 782.0637588500977, :width 718, :height 1015.4567293154772}, :rects ({:x1 87.36979167163372, :y1 741.3844985961914, :x2 616.7273356169462, :y2 755.2734146118164, :width 718, :height 1015.4567293154772} {:x1 87.36979167163372, :y1 768.1749038696289, :x2 576.0654703825712, :y2 782.0637588500977, :width 718, :height 1015.4567293154772}), :page 13}, :content {:text "벡터 b 가 직선 위로 사영되면, 사영 p는 벡터 b 의 해당 직선 방향 부분 이 된다 . 벡터 b가 평면위로 사영되면, 사영 p는 벡터 b의 해당 평면 방향 부분 이 된다. 사영 p는 Pb 이다."}, :properties {:color "yellow"}} {:id #uuid "6a7a041f-7af3-4273-a7e3-c56d9b591165", :page 14, :position {:bounding {:x1 86, :y1 382.9990234375, :x2 660, :y2 453.9990234375, :width 718, :height 1015.4567293154772}, :rects (), :page 14}, :content {:text "[:span]", :image 1786381341457}, :properties {:color "yellow"}} {:id #uuid "6a7a042f-2b0c-4ecd-949e-f28c59939ff2", :page 14, :position {:bounding {:x1 102.31119029223919, :y1 710.7312927246094, :x2 467.52057902514935, :y2 724.6202087402344, :width 718, :height 1015.4567293154772}, :rects ({:x1 102.31119029223919, :y1 710.7312927246094, :x2 467.52057902514935, :y2 724.6202087402344, :width 718, :height 1015.4567293154772}), :page 14}, :content {:text "직선 과 평면 은 단순히 직교 하는 것을 넘어, 서로 직교 여공간 이다"}, :properties {:color "yellow"}} {:id #uuid "6a7a0437-3040-4bc0-a638-f5b5d33a8f99", :page 14, :position {:bounding {:x1 135.98089091479778, :y1 799.5334167480469, :x2 623.7521158903837, :y2 816.8945007324219, :width 718, :height 1015.4567293154772}, :rects ({:x1 135.98089091479778, :y1 799.5334167480469, :x2 623.7521158903837, :y2 816.8945007324219, :width 718, :height 1015.4567293154772}), :page 14}, :content {:text "벡터들은 P1 + P2= b 를 만족 하고, 행렬들은 P+P2= 1, PP2 = 0 을 만족한다 . "}, :properties {:color "yellow"}} {:id #uuid "6a7a043f-522f-490b-b277-c1d2a36f849c", :page 15, :position {:bounding {:x1 379.30771891772747, :y1 407.34588623046875, :x2 620.6924845427275, :y2 421.23480224609375, :width 718, :height 1015.4567293154772}, :rects ({:x1 379.30771891772747, :y1 407.34588623046875, :x2 620.6924845427275, :y2 421.23480224609375, :width 718, :height 1015.4567293154772}), :page 15}, :content {:text " 6 에서 p까지 의 직선 은 벡터 4 와 직교 한다"}, :properties {:color "yellow"}} {:id #uuid "6a7a044a-2260-4606-b890-6f4f9333742c", :page 16, :position {:bounding {:x1 81, :y1 50.4716796875, :x2 667, :y2 166.4716796875, :width 718, :height 1015.4567293154772}, :rects (), :page 16}, :content {:text "[:span]", :image 1786381386523}, :properties {:color "yellow"}} {:id #uuid "6a7a045f-fe09-47a3-b9b0-74e54a3248ee", :page 16, :position {:bounding {:x1 104, :y1 276.4716796875, :x2 508, :y2 317.4716796875, :width 718, :height 1015.4567293154772}, :rects (), :page 16}, :content {:text "[:span]", :image 1786381407053}, :properties {:color "yellow"}} {:id #uuid "6a7a046a-3e0f-494b-b603-5a93cc3eeed4", :page 17, :position {:bounding {:x1 89, :y1 126.2490234375, :x2 604, :y2 207.2490234375, :width 718, :height 1015.4567293154772}, :rects (), :page 17}, :content {:text "[:span]", :image 1786381417724}, :properties {:color "yellow"}} {:id #uuid "6a7af20e-41d5-4040-a603-a53e5809a41f", :page 17, :position {:bounding {:x1 63.465708419680595, :y1 798.9257354736328, :x2 369.44150798022747, :y2 812.8146209716797, :width 718, :height 1015.4567293154772}, :rects ({:x1 63.465708419680595, :y1 798.9257354736328, :x2 369.44150798022747, :y2 812.8146209716797, :width 718, :height 1015.4567293154772}), :page 17}, :content {:text "항등행렬 / 에 대해 행렬 - P 도 사영행렬 이어야 한다"}, :properties {:color "yellow"}} {:id #uuid "6a7af214-6b8f-4d35-99ab-549c781aa104", :page 17, :position {:bounding {:x1 65.47308604419231, :y1 826.5407409667969, :x2 608.8986002653837, :y2 866.1891784667969, :width 718, :height 1015.4567293154772}, :rects ({:x1 85.28645579516888, :y1 826.5407409667969, :x2 608.8986002653837, :y2 839.7351989746094, :width 718, :height 1015.4567293154772} {:x1 65.47308604419231, :y1 851.6058654785156, :x2 102.84287516772747, :y2 866.1891784667969, :width 718, :height 1015.4567293154772}), :page 17}, :content {:text "P 가 하나의 부분공간 위로 사영 할 때 , I -P 는 그 부분 공간과 직교 하는 부분공간 위로 사영 한다."}, :properties {:color "yellow"}} {:id #uuid "6a7af225-e248-4100-b418-ce9559de344b", :page 18, :position {:bounding {:x1 106.54296366870403, :y1 313.35718154907227, :x2 185.54686991870403, :y2 327.94052505493164, :width 718, :height 1015.4567293154772}, :rects ({:x1 106.54296366870403, :y1 313.35718154907227, :x2 185.54686991870403, :y2 327.94052505493164, :width 718, :height 1015.4567293154772}), :page 18}, :content {:text "p = Ai( 사)"}, :properties {:color "yellow"}} {:id #uuid "6a7af22c-331d-4718-b45f-3c7997457022", :page 18, :position {:bounding {:x1 106.54296366870403, :y1 313.35718154907227, :x2 656.6622721403837, :y2 360.95920181274414, :width 718, :height 1015.4567293154772}, :rects ({:x1 288.71528117358685, :y1 313.35718154907227, :x2 656.6622721403837, :y2 327.94052505493164, :width 718, :height 1015.4567293154772} {:x1 106.54296366870403, :y1 343.598087310791, :x2 564.8734537810087, :y2 360.95920181274414, :width 718, :height 1015.4567293154772}), :page 18}, :content {:text "위 의 ' ( hat) 표기는 열 공간 안에서 가장 가까운 벡터 를 제공하는 최적 의 선택 임을 의미 한다 . \" = 1인 경우 , 그 최적 의 선택은 호 - 이다"}, :properties {:color "yellow"}} {:id #uuid "6a7af232-2329-4ae5-8b0b-f32445874c99", :page 18, :position {:bounding {:x1 106.54296366870403, :y1 449.164493560791, :x2 656.1355997771025, :y2 487.836368560791, :width 718, :height 1015.4567293154772}, :rects ({:x1 119.40103404223919, :y1 449.164493560791, :x2 656.1355997771025, :y2 463.74780654907227, :width 718, :height 1015.4567293154772} {:x1 106.54296366870403, :y1 474.6419105529785, :x2 195.51865641772747, :y2 487.836368560791, :width 718, :height 1015.4567293154772}), :page 18}, :content {:text " ( S) 안에서 벡터 을 구하고 , ( C ) 안에서 사영 p= A²을 구한 다음 , (T) 안에서 사영 행렬 P를 구해보자 ."}, :properties {:color "yellow"}} {:id #uuid "6a7af237-5421-4b5e-9aaf-f18ab9f7b198", :page 18, :position {:bounding {:x1 261.27387492358685, :y1 542.133243560791, :x2 497.44590251147747, :y2 556.0220985412598, :width 718, :height 1015.4567293154772}, :rects ({:x1 261.27387492358685, :y1 542.133243560791, :x2 497.44590251147747, :y2 556.0220985412598, :width 718, :height 1015.4567293154772}), :page 18}, :content {:text "오차벡터 b - A '은 부분공간 과 직교한다"}, :properties {:color "yellow"}} {:id #uuid "6a7af245-203a-4d34-99d3-63a1f7a3bc3e", :page 19, :position {:bounding {:x1 60, :y1 120.220703125, :x2 645, :y2 400.220703125, :width 718, :height 1015.4567293154772}, :rects (), :page 19}, :content {:text "[:span]", :image 1786442309180}, :properties {:color "yellow"}} {:id #uuid "6a7af250-44f8-4e4d-8c66-e774cd33390a", :page 19, :position {:bounding {:x1 71.28905741870403, :y1 639.9848022460938, :x2 520.8550211638212, :y2 657.3458862304688, :width 718, :height 1015.4567293154772}, :rects ({:x1 71.28905741870403, :y1 639.9848022460938, :x2 520.8550211638212, :y2 657.3458862304688, :width 718, :height 1015.4567293154772}), :page 19}, :content {:text "핵심 은 정규 방정식 (normal equation ) AT ( b- A² )= 0을 해결 하는 단계이다 ."}, :properties {:color "yellow"}} {:id #uuid "6a7af25d-f986-4721-a903-e7463d07eb9a", :page 19, :position {:bounding {:x1 56, :y1 733.220703125, :x2 645, :y2 888.220703125, :width 718, :height 1015.4567293154772}, :rects (), :page 19}, :content {:text "[:span]", :image 1786442333608}, :properties {:color "yellow"}} {:id #uuid "6a7af267-9dca-45c0-bc40-f0a8db37093b", :page 20, :position {:bounding {:x1 131.39104716479778, :y1 759.5485687255859, :x2 453.23069255053997, :y2 775.5207977294922, :width 718, :height 1015.4567293154772}, :rects ({:x1 131.39104716479778, :y1 759.5485687255859, :x2 453.23069255053997, :y2 775.5207977294922, :width 718, :height 1015.4567293154772}), :page 20}, :content {:text "행렬 P =A ( ATA ) ' A' 를 계산할 때 주의 할 점이 있다"}, :properties {:color "yellow"}} {:id #uuid "6a7af26d-7da7-41db-ba30-fac9454a16e0", :page 20, :position {:bounding {:x1 110.56857554614544, :y1 881.3476409912109, :x2 653.053202316165, :y2 921.2781829833984, :width 718, :height 1015.4567293154772}, :rects ({:x1 110.56857554614544, :y1 881.3476409912109, :x2 653.053202316165, :y2 895.9309539794922, :width 718, :height 1015.4567293154772} {:x1 111.56683604419231, :y1 905.3059539794922, :x2 379.02558390796185, :y2 921.2781829833984, :width 718, :height 1015.4567293154772}), :page 20}, :content {:text "A 는 직사각 행렬 이다. 즉 A의 역행렬은 없다. > 개인 경우에는 A'가 존재하지 않으므로( ATA )' 를 A- '와 ( AT)' 로 나눌 수 없다 "}, :properties {:color "yellow"}} {:id #uuid "6a7af283-66b3-4560-ae49-96b3acabb433", :page 21, :position {:bounding {:x1 119.90017192065716, :y1 157.7582449913025, :x2 559.54856364429, :y2 172.3415732383728, :width 718, :height 1015.4567293154772}, :rects ({:x1 119.90017192065716, :y1 157.7582449913025, :x2 559.54856364429, :y2 172.3415732383728, :width 718, :height 1015.4567293154772}), :page 21}, :content {:text "ATA 가 가역 행렬일 필요충분 조건 은 행렬 A의 열이 선형 독립인 것이다 ."}, :properties {:color "yellow"}} {:id #uuid "6a7af28d-1121-4a8f-94c5-3749f4744e14", :page 22, :position {:bounding {:x1 78, :y1 235.666015625, :x2 671, :y2 458.666015625, :width 718, :height 1015.4567293154772}, :rects (), :page 22}, :content {:text "[:span]", :image 1786442380971}, :properties {:color "yellow"}} {:id #uuid "6a7b0d0a-167b-4f1f-9889-09c8be19e7e0", :page 18, :position {:bounding {:x1 93, :y1 577.443359375, :x2 628, :y2 651.443359375, :width 664.9999999999999, :height 940.4996169843904}, :rects (), :page 18}, :content {:text "[:span]", :image 1786449160532}, :properties {:color "yellow"}} {:id #uuid "6a7b0d23-2b91-414c-a5e2-50a025e0a7ba", :page 21, :position {:bounding {:x1 105, :y1 484.5546875, :x2 509, :y2 518.5546875, :width 664.9999999999999, :height 940.4996169843904}, :rects (), :page 21}, :content {:text "[:span]", :image 1786449187251}, :properties {:color "yellow"}} {:id #uuid "6a7b0d35-505d-4e2b-89fb-270f4e5f86de", :page 15, :position {:bounding {:x1 41, :y1 417.5546875, :x2 586, :y2 618.5546875, :width 664.9999999999999, :height 940.4996169843904}, :rects (), :page 15}, :content {:text "[:span]", :image 1786449205469}, :properties {:color "yellow"}} {:id #uuid "6a7dcf45-30e9-47fc-bc0f-3243c1c73a00", :page 28, :position {:bounding {:x1 101.67100524902344, :y1 606.2066040039062, :x2 647.9697265625, :y2 677.6258544921875, :width 716, :height 1012.6281590388325}, :rects ({:x1 232.33506774902344, :y1 606.2066040039062, :x2 647.9697265625, :y2 619.4010009765625, :width 716, :height 1012.6281590388325} {:x1 101.67100524902344, :y1 632.7473754882812, :x2 647.9671020507812, :y2 650.1084594726562, :width 716, :height 1012.6281590388325} {:x1 102.66926574707031, :y1 663.7369384765625, :x2 208.1149139404297, :y2 677.6258544921875, :width 716, :height 1012.6281590388325}), :page 28}, :content {:text "오차벡터 e= b-Az 를 항상 0으로 줄일 수 는 없다. e가 0일 때 그는 Az = b의 정확한 해이다. 의 크기가 가능한 한 작아서 116 - A ||' 이 최솟값에 도달하면 , 굳은최소제곱 해가 된다"}, :properties {:color "yellow"}} {:id #uuid "6a7dcf4f-ec05-4a72-afd6-26fe3bde7f0b", :page 28, :position {:bounding {:x1 241.21092224121094, :y1 758.0512084960938, :x2 549.0007934570312, :y2 774.0234375, :width 716, :height 1012.6281590388325}, :rects ({:x1 241.21092224121094, :y1 758.0512084960938, :x2 549.0007934570312, :y2 774.0234375, :width 716, :height 1012.6281590388325}), :page 28}, :content {:text "기본 방정식은 여전히 정규 방정식 AT A²= ATb 이다"}, :properties {:color "yellow"}} {:id #uuid "6a7dcf53-01d5-412b-9d65-325536a9a5d7", :page 28, :position {:bounding {:x1 117.5564193725586, :y1 840.0064697265625, :x2 635.0550537109375, :y2 854.5897827148438, :width 716, :height 1012.6281590388325}, :rects ({:x1 117.5564193725586, :y1 840.0064697265625, :x2 635.0550537109375, :y2 854.5897827148438, :width 716, :height 1012.6281590388325}), :page 28}, :content {:text "Az= b의 해 가 존재하지 않으면, 이 식의 양변에 AT 를 곱하고 AT Af= ATb를 푼다."}, :properties {:color "yellow"}} {:id #uuid "6a7dd176-75b8-4e9f-bbf4-25909045ec4e", :page 30, :position {:bounding {:x1 190.31031799316406, :y1 406.54296112060547, :x2 563.4765625, :y2 421.4409713745117, :width 716, :height 1012.6281590388325}, :rects ({:x1 362.43487548828125, :y1 406.54296112060547, :x2 563.4765625, :y2 420.4318161010742, :width 716, :height 1012.6281590388325} {:x1 190.31031799316406, :y1 407.5520553588867, :x2 336.9357604980469, :y2 421.4409713745117, :width 716, :height 1012.6281590388325}), :page 30}, :content {:text "임의 의 에 대한 제곱 오차 ||| Az- 6 ||=|| Azp ||+ ||e || 2"}, :properties {:color "yellow"}} {:id #uuid "6a7dd17a-8e52-4cec-b72c-eab898415e99", :page 30, :position {:bounding {:x1 202.19183349609375, :y1 593.8476486206055, :x2 556.54296875, :y2 609.8198776245117, :width 716, :height 1012.6281590388325}, :rects ({:x1 202.19183349609375, :y1 593.8476486206055, :x2 556.54296875, :y2 609.8198776245117, :width 716, :height 1012.6281590388325}), :page 30}, :content {:text "최소제곱 해 소은 E = ||A -6 ||' 을 가능한 한 작게 만든다 "}, :properties {:color "yellow"}} {:id #uuid "6a7f09e3-c19c-4ff6-b00d-d73ac7b9cc59", :page 31, :position {:bounding {:x1 136.61024475097656, :y1 582.4977951049805, :x2 333.3098449707031, :y2 595.692253112793, :width 716, :height 1012.6281590388325}, :rects ({:x1 136.61024475097656, :y1 582.4977951049805, :x2 333.3098449707031, :y2 595.692253112793, :width 716, :height 1012.6281590388325}), :page 31}, :content {:text "미분 적분학 의 관점에서 생각해보자"}, :properties {:color "yellow"}} {:id #uuid "6a7f0a0d-c7d0-4ebe-b4a7-c2d23caaf25b", :page 32, :position {:bounding {:x1 201.83375549316406, :y1 436.72959899902344, :x2 542.3562622070312, :y2 453.39622497558594, :width 716, :height 1012.6281590388325}, :rects ({:x1 201.83375549316406, :y1 436.72959899902344, :x2 542.3562622070312, :y2 453.39622497558594, :width 716, :height 1012.6281590388325}), :page 32}, :content {:text "ATAE= AT6 일 때 , || Az - 611 '의 편도함수는 0 이다"}, :properties {:color "yellow"}} {:id #uuid "6a7f0a47-3114-4b81-af6e-2818eeafc72a", :page 32, :position {:bounding {:x1 95.00867462158203, :y1 321.9509735107422, :x2 352.0469970703125, :y2 338.6175994873047, :width 716, :height 1012.6281590388325}, :rects ({:x1 95.00867462158203, :y1 321.9509735107422, :x2 352.0469970703125, :y2 338.6175994873047, :width 716, :height 1012.6281590388325}), :page 32}, :content {:text "식 (4 )의 두 방정식은 ATA=ATb이다."}, :properties {:color "yellow"}} {:id #uuid "6a7f0a6c-2e57-4d5b-beef-04a0a0062d19", :page 32, :position {:bounding {:x1 94, :y1 206.748046875, :x2 676, :y2 307.748046875, :width 716, :height 1012.6281590388325}, :rects (), :page 32}, :content {:text "[:span]", :image 1786710636598}, :properties {:color "yellow"}} {:id #uuid "6a7f0a74-30ff-4ec4-ba78-52d533dd1f8d", :page 31, :position {:bounding {:x1 109, :y1 689.498046875, :x2 639, :y2 726.498046875, :width 716, :height 1012.6281590388325}, :rects (), :page 31}, :content {:text "[:span]", :image 1786710644409}, :properties {:color "yellow"}} {:id #uuid "6a7f0aac-af80-47bc-9b60-cd999da58ec2", :page 32, :position {:bounding {:x1 99.01258087158203, :y1 781.5538024902344, :x2 484.52642822265625, :y2 795.4426574707031, :width 716, :height 1012.6281590388325}, :rects ({:x1 99.01258087158203, :y1 781.5538024902344, :x2 484.52642822265625, :y2 795.4426574707031, :width 716, :height 1012.6281590388325}), :page 32}, :content {:text "Az= b대신 에 Ai =p 를 푼다. 오차 e=b - p 는 피할 수 없다."}, :properties {:color "yellow"}} {:id #uuid "6a7f0ade-00e5-4727-942b-d85312b043db", :page 33, :position {:bounding {:x1 66.22178649902344, :y1 411.4040832519531, :x2 611.9248657226562, :y2 480.6857604980469, :width 716, :height 1012.6281590388325}, :rects ({:x1 66.22178649902344, :y1 411.4040832519531, :x2 609.2098999023438, :y2 424.5984802246094, :width 716, :height 1012.6281590388325} {:x1 66.22178649902344, :y1 439.2577819824219, :x2 606.2931518554688, :y2 453.1466979980469, :width 716, :height 1012.6281590388325} {:x1 66.22178649902344, :y1 466.1023864746094, :x2 611.9248657226562, :y2 480.6857604980469, :width 716, :height 1012.6281590388325}), :page 33}, :content {:text "영공간 N (A ) 가 얼마나 작은지에 주목하라 . N( A) 는 단 하나 의 점만 포함 한다. 선형독립 인 열을이용 하면 Az= 0의 유일한 해 는 z = 0임을 알 수 있다. 그러면 ATA 는 가역행렬이다. 방정식 ATA = ATb는 최적의 벡터 눈을 완전히 결정 한다. 오차e= b-p는 ATe= 0을 만족 한다 "}, :properties {:color "yellow"}} {:id #uuid "6a7f0b52-edff-4a79-a474-8007acbfaf55", :page 33, :position {:bounding {:x1 66.22178649902344, :y1 647.6344909667969, :x2 458.88372802734375, :y2 664.9956359863281, :width 716, :height 1012.6281590388325}, :rects ({:x1 66.22178649902344, :y1 647.6344909667969, :x2 458.88372802734375, :y2 664.9956359863281, :width 716, :height 1012.6281590388325}), :page 33}, :content {:text "직선 맞추기 (fitting a line) 는 최소 제곱 법에 대한 가장 명확한 응용 이다"}, :properties {:color "yellow"}} {:id #uuid "6a7f0d62-7ece-49bd-8feb-0343d9b2524c", :page 38, :position {:bounding {:x1 100.37976837158203, :y1 68.52212524414062, :x2 483.2030944824219, :y2 87.96658325195312, :width 716, :height 1012.6281590388325}, :rects ({:x1 100.37976837158203, :y1 68.52212524414062, :x2 483.2030944824219, :y2 87.96658325195312, :width 716, :height 1012.6281590388325}), :page 38}, :content {:text "푸리에 급수(Fourier series)는 무한 차원 에서 의 최소제곱 문제이다 "}, :properties {:color "yellow"}} {:id #uuid "6a7f15b4-5473-4aab-a20c-7938633ae8f5", :page 34, :position {:bounding {:x1 113.2595443725586, :y1 755.9244537353516, :x2 659.7547607421875, :y2 799.3923492431641, :width 716, :height 1012.6281590388325}, :rects ({:x1 482.07464599609375, :y1 755.9244537353516, :x2 659.7547607421875, :y2 770.5077667236328, :width 716, :height 1012.6281590388325} {:x1 113.2595443725586, :y1 785.5034332275391, :x2 397.78643798828125, :y2 799.3923492431641, :width 716, :height 1012.6281590388325}), :page 34}, :content {:text "오차벡터 e ( 즉 잔차(residual ) b -A² )는 행렬 A의 열과 직교 한다( 기하학 관점 )"}, :properties {:color "yellow"}} {:id #uuid "6a7f15c9-4514-48df-a2a8-86fc14eb92c4", :page 34, :position {:bounding {:x1 115, :y1 681.52734375, :x2 668, :y2 748.52734375, :width 716, :height 1012.6281590388325}, :rects (), :page 34}, :content {:text "[:span]", :image 1786713545633}, :properties {:color "yellow"}} {:id #uuid "6a7f15e6-50ab-4391-aeda-acda5434850c", :page 36, :position {:bounding {:x1 106, :y1 219.0546875, :x2 659, :y2 344.0546875, :width 716, :height 1012.6281590388325}, :rects (), :page 36}, :content {:text "[:span]", :image 1786713574364}, :properties {:color "yellow"}} {:id #uuid "6a82e162-84c7-46ef-bcdf-96db71e7c22f", :page 45, :position {:bounding {:x1 166.17837524414062, :y1 692.0029945373535, :x2 533.9240112304688, :y2 708.6696815490723, :width 716, :height 1012.6281590388325}, :rects ({:x1 166.17837524414062, :y1 692.0029945373535, :x2 533.9240112304688, :y2 708.6696815490723, :width 716, :height 1012.6281590388325}), :page 45}, :content {:text "기저는 벡터공간을 생성 하는 선형독립인 벡터들 로 구성 된다."}, :properties {:color "yellow"}} {:id #uuid "6a82e178-6b2a-41fd-8096-b20b2403e67d", :page 45, :position {:bounding {:x1 71.31076049804688, :y1 809.4075355529785, :x2 622.91259765625, :y2 884.8415565490723, :width 716, :height 1012.6281590388325}, :rects ({:x1 72.30902862548828, :y1 809.4075355529785, :x2 622.91259765625, :y2 823.9908485412598, :width 716, :height 1012.6281590388325} {:x1 71.31076049804688, :y1 841.015567779541, :x2 619.9304809570312, :y2 855.5989418029785, :width 716, :height 1012.6281590388325} {:x1 72.30902862548828, :y1 868.869327545166, :x2 384.1726379394531, :y2 884.8415565490723, :width 716, :height 1012.6281590388325}), :page 45}, :content {:text "내적 9. 9가 모두 0일 때 91 ... 9 개 은 서로 직교한다 . 좀 더 정확히 말하면 ≠ 일 때만 qq=0 이다. 한발 더 나아가 각 벡터 91 ... 9 들을 자기 자신 의 크기 로 나누면 정규직교벡터 가 된다. 이를 통해 모든 벡터 의 크기 는 1 이 된다"}, :properties {:color "yellow"}} {:id #uuid "6a82e18d-e2f1-470d-a591-ff79a4513fc0", :page 46, :position {:bounding {:x1 89.69444441795349, :y1 58, :x2 667.6944444179535, :y2 260, :width 716, :height 1012.6281590388325}, :rects (), :page 46}, :content {:text "[:span]", :image 1786962317060}, :properties {:color "yellow"}} {:id #uuid "6a82e195-abe4-45cf-8c36-23ba4aa08b4f", :page 46, :position {:bounding {:x1 349.1102159023285, :y1 313.55250549316406, :x2 497.0246751308441, :y2 327.44142150878906, :width 716, :height 1012.6281590388325}, :rects ({:x1 349.1102159023285, :y1 313.55250549316406, :x2 497.0246751308441, :y2 327.44142150878906, :width 716, :height 1012.6281590388325}), :page 46}, :content {:text "일반적으로 QQT≠ 이다"}, :properties {:color "yellow"}} {:id #uuid "6a82e19e-e3d4-4685-b9f9-b9e1bc804816", :page 46, :position {:bounding {:x1 100.73784041404724, :y1 550.4882965087891, :x2 653.0381944179535, :y2 595.5728912353516, :width 716, :height 1012.6281590388325}, :rects ({:x1 510.351548910141, :y1 550.4882965087891, :x2 653.0381944179535, :y2 567.1549224853516, :width 716, :height 1012.6281590388325} {:x1 100.73784041404724, :y1 581.6840362548828, :x2 473.280259847641, :y2 595.5728912353516, :width 716, :height 1012.6281590388325}), :page 46}, :content {:text "Q가 정사각행렬 일 때 , QQ=1이면 QT= Q-' 이다. 즉 ( 전치행렬)= (역행렬 ) 이다"}, :properties {:color "yellow"}} {:id #uuid "6a82e1a7-0965-48c5-a35a-772b3daba33d", :page 46, :position {:bounding {:x1 100.73784041404724, :y1 619.2708282470703, :x2 648.2964341640472, :y2 659.9066925048828, :width 716, :height 1012.6281590388325}, :rects ({:x1 100.73784041404724, :y1 619.2708282470703, :x2 648.2964341640472, :y2 633.1596832275391, :width 716, :height 1012.6281590388325} {:x1 100.73784041404724, :y1 646.0177764892578, :x2 179.6332414150238, :y2 659.9066925048828, :width 716, :height 1012.6281590388325}), :page 46}, :content {:text "열 들이 정규성 은 만족 하지 않고 직교성 만 만족하는 경우, 내적은 여전히 대각 행렬( 항등 행렬은 아님) 을 만든다 "}, :properties {:color "yellow"}} {:id #uuid "6a82e1b4-386d-4371-b3b6-cd50d2cfeafe", :page 46, :position {:bounding {:x1 211.56683349609375, :y1 710.7421417236328, :x2 498.0073547363281, :y2 727.4088287353516, :width 716, :height 1012.6281590388325}, :rects ({:x1 211.56683349609375, :y1 710.7421417236328, :x2 498.0073547363281, :y2 727.4088287353516, :width 716, :height 1012.6281590388325}), :page 46}, :content {:text "Q 가 직사각 행렬이라고 해도 QQ=I는 성립 한다"}, :properties {:color "yellow"}} {:id #uuid "6a82e1bf-dd4a-4c0a-8c28-174d9da0d74b", :page 46, :position {:bounding {:x1 234.34243774414062, :y1 739.6158599853516, :x2 481.2337341308594, :y2 756.9769439697266, :width 716, :height 1012.6281590388325}, :rects ({:x1 234.34243774414062, :y1 739.6158599853516, :x2 481.2337341308594, :y2 756.9769439697266, :width 716, :height 1012.6281590388325}), :page 46}, :content {:text "만약 Q 가 정사각행렬이면 QQT =/ 도 성립"}, :properties {:color "yellow"}} {:id #uuid "6a82e1c3-f8af-452a-bb90-bbfd4bd80ae9", :page 46, :position {:bounding {:x1 453.005615234375, :y1 769.8025054931641, :x2 619.2484130859375, :y2 784.3858184814453, :width 716, :height 1012.6281590388325}, :rects ({:x1 453.005615234375, :y1 769.8025054931641, :x2 619.2484130859375, :y2 784.3858184814453, :width 716, :height 1012.6281590388325}), :page 46}, :content {:text "Q 의 역행렬 은 전치행렬 QT"}, :properties {:color "yellow"}} {:id #uuid "6a82e1d1-ceda-425e-9ef1-24dcf5e0ee08", :page 46, :position {:bounding {:x1 99.72872924804688, :y1 797.1570587158203, :x2 405.6857604980469, :y2 810.3515167236328, :width 716, :height 1012.6281590388325}, :rects ({:x1 99.72872924804688, :y1 797.1570587158203, :x2 405.6857604980469, :y2 810.3515167236328, :width 716, :height 1012.6281590388325}), :page 46}, :content {:text "이와 같은 경우 정사각 행렬 Q를 직교행렬 이라 한다."}, :properties {:color "yellow"}} {:id #uuid "6a82e1e1-08da-4c9c-a290-6adfb66f7b0b", :page 47, :position {:bounding {:x1 64.6484375, :y1 66.77516174316406, :x2 630.5012817382812, :y2 114.70268249511719, :width 716, :height 1012.6281590388325}, :rects ({:x1 594.9110107421875, :y1 66.77516174316406, :x2 630.5012817382812, :y2 83.44184875488281, :width 716, :height 1012.6281590388325} {:x1 64.6484375, :y1 95.25825500488281, :x2 462.85089111328125, :y2 114.70268249511719, :width 716, :height 1012.6281590388325}), :page 47}, :content {:text "직교행렬인지 를 빠르게 판정 하는 방법은 QTQ=1 인지 확인하는 것이다"}, :properties {:color "yellow"}} {:id #uuid "6a82e1f4-6c26-433e-b727-be8bfd60e96f", :page 48, :position {:bounding {:x1 281.8142395019531, :y1 130.3927879333496, :x2 459.3993225097656, :y2 143.58723068237305, :width 716, :height 1012.6281590388325}, :rects ({:x1 281.8142395019531, :y1 130.3927879333496, :x2 459.3993225097656, :y2 143.58723068237305, :width 716, :height 1012.6281590388325}), :page 48}, :content {:text "모든 치환행렬 은 직교행렬이다"}, :properties {:color "yellow"}} {:id #uuid "6a82e267-3148-4a25-8b7c-9f8fa7547998", :page 48, :position {:bounding {:x1 102.8103256225586, :y1 629.6006469726562, :x2 652.6907958984375, :y2 676.736083984375, :width 716, :height 1012.6281590388325}, :rects ({:x1 102.8103256225586, :y1 629.6006469726562, :x2 652.6907958984375, :y2 646.267333984375, :width 716, :height 1012.6281590388325} {:x1 103.80858612060547, :y1 658.6805419921875, :x2 423.3615417480469, :y2 676.736083984375, :width 716, :height 1012.6281590388325}), :page 48}, :content {:text "회전 은 모든 벡터 의 크기를 유지 한다. 반사와 치환도 마찬가지 이다. 그러므로 행렬 Q를 곱한다고해도 벡터의 크기와 벡터 간의 사잇각 은 변하지 않는다 "}, :properties {:color "yellow"}} {:id #uuid "6a82e26d-cefd-4963-ad7c-5340a6d2cc01", :page 48, :position {:bounding {:x1 115.7009506225586, :y1 658.6805419921875, :x2 647.3958129882812, :y2 703.2443237304688, :width 716, :height 1012.6281590388325}, :rects ({:x1 559.7547607421875, :y1 658.6805419921875, :x2 647.3958129882812, :y2 676.736083984375, :width 716, :height 1012.6281590388325} {:x1 115.7009506225586, :y1 688.6610107421875, :x2 445.50860595703125, :y2 703.2443237304688, :width 716, :height 1012.6281590388325}), :page 48}, :content {:text "(Qz) ( Qz) = QQ = TI=IT] 이므로, Qz ' 은 || ||' 과 같음"}, :properties {:color "yellow"}} {:id #uuid "6a82e278-4ece-4377-a3eb-5c7e51f41f88", :page 48, :position {:bounding {:x1 288.7586669921875, :y1 803.2334899902344, :x2 487.55322265625, :y2 817.1223754882812, :width 716, :height 1012.6281590388325}, :rects ({:x1 288.7586669921875, :y1 803.2334899902344, :x2 487.55322265625, :y2 817.1223754882812, :width 716, :height 1012.6281590388325}), :page 48}, :content {:text "모든 벡터 2에 대해 ||Q || =|||||"}, :properties {:color "yellow"}} {:id #uuid "6a82e27d-5d9b-45d7-abb7-538d4900b18a", :page 48, :position {:bounding {:x1 284.8198547363281, :y1 890.3536987304688, :x2 472.7052001953125, :y2 904.2425842285156, :width 716, :height 1012.6281590388325}, :rects ({:x1 284.8198547363281, :y1 890.3536987304688, :x2 472.7052001953125, :y2 904.2425842285156, :width 716, :height 1012.6281590388325}), :page 48}, :content {:text "(Qx) (Qy) = xQTQy=xTy"}, :properties {:color "yellow"}} {:id #uuid "6a82e28c-5f81-4475-85e9-16bbd2dfa773", :page 49, :position {:bounding {:x1 66.5798568725586, :y1 348.69791412353516, :x2 475.7702941894531, :y2 365.3645706176758, :width 716, :height 1012.6281590388325}, :rects ({:x1 66.5798568725586, :y1 348.69791412353516, :x2 475.7702941894531, :y2 365.3645706176758, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "Qz=b 의 최소 제곱 해는 i =Q6 이다. 그리고 사영행렬은 QQ \" 이다"}, :properties {:color "yellow"}} {:id #uuid "6a82e292-e2e2-461b-aa6b-9b20b081c9cd", :page 49, :position {:bounding {:x1 268.4244689941406, :y1 446.35416412353516, :x2 415.0932922363281, :y2 460.9374771118164, :width 716, :height 1012.6281590388325}, :rects ({:x1 268.4244689941406, :y1 446.35416412353516, :x2 415.0932922363281, :y2 460.9374771118164, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "ATA는 이제 QQ =I "}, :properties {:color "yellow"}} {:id #uuid "6a82e299-2ec8-4c15-b064-5af3e9eca2e6", :page 49, :position {:bounding {:x1 396.0828857421875, :y1 476.03079986572266, :x2 544.4912109375, :y2 490.6141128540039, :width 716, :height 1012.6281590388325}, :rects ({:x1 396.0828857421875, :y1 476.03079986572266, :x2 544.4912109375, :y2 490.6141128540039, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "사영은 p = Qi=QQTb"}, :properties {:color "yellow"}} {:id #uuid "6a82e2b6-0d7e-4b09-bc31-3a3910ee76a1", :page 49, :position {:bounding {:x1 60, :y1 507.21875, :x2 611, :y2 599.21875, :width 716, :height 1012.6281590388325}, :rects (), :page 49}, :content {:text "[:span]", :image 1786962613749}, :properties {:color "yellow"}} {:id #uuid "6a82e2bd-91fe-4503-b79b-dd434a306690", :page 49, :position {:bounding {:x1 65.58159637451172, :y1 619.0646743774414, :x2 601.884033203125, :y2 664.6484146118164, :width 716, :height 1012.6281590388325}, :rects ({:x1 254.60067749023438, :y1 619.0646743774414, :x2 601.884033203125, :y2 637.1202163696289, :width 716, :height 1012.6281590388325} {:x1 65.58159637451172, :y1 650.0651016235352, :x2 90.32429504394531, :y2 664.6484146118164, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "Q 가 정사각행렬 ( = \"인 경우 )이면 , 부분공간 은 전체 공간이된다."}, :properties {:color "yellow"}} {:id #uuid "6a82e2c6-865c-4ea8-92ab-4ffb5985120b", :page 49, :position {:bounding {:x1 65.58159637451172, :y1 650.0651016235352, :x2 603.8912353515625, :y2 720.8224258422852, :width 716, :height 1012.6281590388325}, :rects ({:x1 433.669677734375, :y1 650.0651016235352, :x2 602.92138671875, :y2 664.6484146118164, :width 716, :height 1012.6281590388325} {:x1 65.58159637451172, :y1 679.1340713500977, :x2 603.8912353515625, :y2 695.8007583618164, :width 716, :height 1012.6281590388325} {:x1 65.58159637451172, :y1 709.0168838500977, :x2 110.36241149902344, :y2 720.8224258422852, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "이때 해는 근사해가 아닌 정확한 해 이다. 벡터 b 의 전체 공간 위로 의 사영 은 자기 자신 이다. 이 경우 p = b.P= QQT=1가 된다 "}, :properties {:color "yellow"}} {:id #uuid "6a82e305-2b46-4fa9-8882-17831bc270ab", :page 49, :position {:bounding {:x1 64.6484375, :y1 745.1822891235352, :x2 602.1050415039062, :y2 787.3263320922852, :width 716, :height 1012.6281590388325}, :rects ({:x1 496.03948974609375, :y1 745.1822891235352, :x2 602.1050415039062, :y2 761.1544570922852, :width 716, :height 1012.6281590388325} {:x1 64.6484375, :y1 772.7430191040039, :x2 372.83001708984375, :y2 787.3263320922852, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "p= 6 일 때 , 우리 의공식은 b 를 1차원 사영 들을 모아 놓은 것으로 조합한다"}, :properties {:color "yellow"}} {:id #uuid "6a82e30a-a62c-41da-990a-4a283a143677", :page 49, :position {:bounding {:x1 302.0724792480469, :y1 805.2516860961914, :x2 571.6145629882812, :y2 819.1406021118164, :width 716, :height 1012.6281590388325}, :rects ({:x1 302.0724792480469, :y1 805.2516860961914, :x2 571.6145629882812, :y2 819.1406021118164, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "모든 b =QQb는 9.들을 따라 사영 한 것들의 합"}, :properties {:color "yellow"}} {:id #uuid "6a82e31e-fa46-47bb-b43d-fcba124367c7", :page 49, :position {:bounding {:x1 183.6944444179535, :y1 828.5546875, :x2 614.6944444179535, :y2 864.5546875, :width 716, :height 1012.6281590388325}, :rects (), :page 49}, :content {:text "[:span]", :image 1786962718092}, :properties {:color "yellow"}} {:id #uuid "6a82e326-de72-4c68-a7ac-d3b895eb174d", :page 49, :position {:bounding {:x1 125.93315291404724, :y1 906.1523284912109, :x2 481.9227159023285, :y2 920.0411834716797, :width 716, :height 1012.6281590388325}, :rects ({:x1 125.93315291404724, :y1 906.1523284912109, :x2 481.9227159023285, :y2 920.0411834716797, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "변환 은 벡터 & 또는 함수 f(r )를 직교 하는 조각 들로 분해 한다 "}, :properties {:color "yellow"}} {:id #uuid "6a82e32e-25cb-436e-8a86-7b6d5f2d6bd7", :page 49, :position {:bounding {:x1 487.0876634120941, :y1 906.1523284912109, :x2 598.9202744960785, :y2 920.0411834716797, :width 716, :height 1012.6281590388325}, :rects ({:x1 487.0876634120941, :y1 906.1523284912109, :x2 598.9202744960785, :y2 920.0411834716797, :width 716, :height 1012.6281590388325}), :page 49}, :content {:text "그다음 식 (6) 에서와"}, :properties {:color "yellow"}} {:id #uuid "6a82e333-e145-4d1a-a680-a2e1050a199b", :page 50, :position {:bounding {:x1 318.39190673828125, :y1 178.80859375, :x2 322.6779479980469, :y2 187.14193725585938, :width 716, :height 1012.6281590388325}, :rects ({:x1 318.39190673828125, :y1 178.80859375, :x2 322.6779479980469, :y2 187.14193725585938, :width 716, :height 1012.6281590388325}), :page 50}, :content {:text "1"}, :properties {:color "yellow"}} {:id #uuid "6a82e33e-03b7-4ef8-b756-8b421ac4cd8b", :page 50, :position {:bounding {:x1 102.8103256225586, :y1 70.83332824707031, :x2 534.66796875, :y2 88.19444274902344, :width 716, :height 1012.6281590388325}, :rects ({:x1 102.8103256225586, :y1 70.83332824707031, :x2 534.66796875, :y2 88.19444274902344, :width 716, :height 1012.6281590388325}), :page 50}, :content {:text "같이 조각 들을 합침으로써 , 역변환 은 b 또는 ( z )를 원래대로 되 돌린다 "}, :properties {:color "yellow"}} {:id #uuid "6a82e3ab-ae59-4678-9572-e372565f69b8", :page 50, :position {:bounding {:x1 110.76388549804688, :y1 807.08544921875, :x2 356.02703857421875, :y2 820.2799072265625, :width 716, :height 1012.6281590388325}, :rects ({:x1 110.76388549804688, :y1 807.08544921875, :x2 356.02703857421875, :y2 820.2799072265625, :width 716, :height 1012.6281590388325}), :page 50}, :content {:text "그림 - 슈미트 과정 은 A= 4 로 놓고 시작한다"}, :properties {:color "yellow"}} {:id #uuid "6a82e3d0-5802-46a0-83ea-ddcfc4da62ac", :page 50, :position {:bounding {:x1 367.87109375, :y1 807.08544921875, :x2 554.349609375, :y2 820.2799072265625, :width 716, :height 1012.6281590388325}, :rects ({:x1 367.87109375, :y1 807.08544921875, :x2 554.349609375, :y2 820.2799072265625, :width 716, :height 1012.6281590388325}), :page 50}, :content {:text "첫 번째 방향은 그대로 받아 들인다"}, :properties {:color "yellow"}} {:id #uuid "6a82e3d3-fd4b-4005-9c80-6e2e682944ed", :page 50, :position {:bounding {:x1 110.76388549804688, :y1 807.08544921875, :x2 657.6654052734375, :y2 847.0160522460938, :width 716, :height 1012.6281590388325}, :rects ({:x1 566.6340942382812, :y1 807.08544921875, :x2 657.6654052734375, :y2 820.2799072265625, :width 716, :height 1012.6281590388325} {:x1 110.76388549804688, :y1 833.8215942382812, :x2 226.19357299804688, :y2 847.0160522460938, :width 716, :height 1012.6281590388325}), :page 50}, :content {:text "다음 방향 B 는 A 와 직교 해야 한다 "}, :properties {:color "yellow"}} {:id #uuid "6a82e3d8-90ed-4dd1-b6dd-dee4d0affe72", :page 50, :position {:bounding {:x1 357.9969482421875, :y1 833.8215942382812, :x2 543.4352416992188, :y2 847.0160522460938, :width 716, :height 1012.6281590388325}, :rects ({:x1 357.9969482421875, :y1 833.8215942382812, :x2 543.4352416992188, :y2 847.0160522460938, :width 716, :height 1012.6281590388325}), :page 50}, :content {:text "6에서 6의 A 위로의 사영을 뺀다"}, :properties {:color "yellow"}} {:id #uuid "6a82e3dc-f30b-4555-9e11-13a72e8a2863", :page 50, :position {:bounding {:x1 111.76214599609375, :y1 833.8215942382812, :x2 655.68359375, :y2 872.5260009765625, :width 716, :height 1012.6281590388325}, :rects ({:x1 598.2747192382812, :y1 833.8215942382812, :x2 655.68359375, :y2 847.0160522460938, :width 716, :height 1012.6281590388325} {:x1 111.76214599609375, :y1 858.6371459960938, :x2 375.29248046875, :y2 872.5260009765625, :width 716, :height 1012.6281590388325}), :page 50}, :content {:text "A와 직교하는 부분 이 남는데 , 이것이 바로 벡터 B이다"}, :properties {:color "yellow"}} {:id #uuid "6a82e3e5-5800-483c-8b51-efa352d4f752", :page 51, :position {:bounding {:x1 61, :y1 49.88671875, :x2 625, :y2 136.88671875, :width 716, :height 1012.6281590388325}, :rects (), :page 51}, :content {:text "[:span]", :image 1786962917582}, :properties {:color "yellow"}} {:id #uuid "6a82e3ee-e4b1-4abb-b944-108a14913c54", :page 51, :position {:bounding {:x1 245.72482299804688, :y1 279.9153747558594, :x2 504.9721984863281, :y2 293.8042297363281, :width 716, :height 1012.6281590388325}, :rects ({:x1 245.72482299804688, :y1 279.9153747558594, :x2 504.9721984863281, :y2 293.8042297363281, :width 716, :height 1012.6281590388325}), :page 51}, :content {:text "세 번째 방향 은 A와 B 의 선형결합이 아니다"}, :properties {:color "yellow"}} {:id #uuid "6a82e3f9-2f43-481a-b2c3-0be70ba2de43", :page 51, :position {:bounding {:x1 62.641056060791016, :y1 307.4653015136719, :x2 618.671142578125, :y2 347.4067077636719, :width 716, :height 1012.6281590388325}, :rects ({:x1 538.5633544921875, :y1 307.4653015136719, :x2 618.671142578125, :y2 320.6596984863281, :width 716, :height 1012.6281590388325} {:x1 62.641056060791016, :y1 334.2122497558594, :x2 417.89935302734375, :y2 347.4067077636719, :width 716, :height 1012.6281590388325}), :page 51}, :content {:text "그러므로 다음과 같이 C 에서 A. B 방향 의 성분 을 뺌 으로써 C 를 얻는다"}, :properties {:color "yellow"}} {:id #uuid "6a82e3ff-5b89-4d94-bb95-b56e057416e6", :page 51, :position {:bounding {:x1 51, :y1 368.33203125, :x2 622, :y2 439.33203125, :width 716, :height 1012.6281590388325}, :rects (), :page 51}, :content {:text "[:span]", :image 1786962943281}, :properties {:color "yellow"}} {:id #uuid "6a82e41a-b11f-4419-8e8b-c245e51a5a97", :page 51, :position {:bounding {:x1 62.641056060791016, :y1 461.6427459716797, :x2 615.700927734375, :y2 500.77037048339844, :width 716, :height 1012.6281590388325}, :rects ({:x1 443.5546569824219, :y1 461.6427459716797, :x2 615.700927734375, :y2 473.44834899902344, :width 716, :height 1012.6281590388325} {:x1 62.641056060791016, :y1 487.57591247558594, :x2 456.1740417480469, :y2 500.77037048339844, :width 716, :height 1012.6281590388325}), :page 51}, :content {:text "새로운 벡터를 기존에 구한 직교하 는 벡터 들 위로 사영하여 , 그 성분 들을 새로운 벡터에서 뺀다 ."}, :properties {:color "yellow"}} {:id #uuid "6a82e422-a27d-4bcb-8b5d-e1686b0bb1bb", :page 51, :position {:bounding {:x1 130.94618225097656, :y1 540.2560272216797, :x2 421.32061767578125, :y2 554.8394012451172, :width 716, :height 1012.6281590388325}, :rects ({:x1 130.94618225097656, :y1 540.2560272216797, :x2 421.32061767578125, :y2 554.8394012451172, :width 716, :height 1012.6281590388325}), :page 51}, :content {:text "직교벡터 A. B. C. D를 각각 의 크기로 나눈다"}, :properties {:color "yellow"}} {:id #uuid "6a82e460-742e-406f-b5d3-26daef798a8b", :page 52, :position {:bounding {:x1 106.74913024902344, :y1 794.216552734375, :x2 653.7927856445312, :y2 833.94091796875, :width 716, :height 1012.6281590388325}, :rects ({:x1 106.74913024902344, :y1 794.216552734375, :x2 653.7927856445312, :y2 807.4110107421875, :width 716, :height 1012.6281590388325} {:x1 108.68054962158203, :y1 820.0520629882812, :x2 241.72964477539062, :y2 833.94091796875, :width 716, :height 1012.6281590388325}), :page 52}, :content {:text "연결하는 세 번째 행렬 이 존재한다 . 이 세 번째 행렬이 A= QR에 있는 삼각행렬 R 이다 (이는1장 에서의 R 이 아니다)"}, :properties {:color "yellow"}} {:id #uuid "6a82e468-4403-4612-8d6e-56b4137155ab", :page 53, :position {:bounding {:x1 142.9036407470703, :y1 68.60894775390625, :x2 577.541259765625, :y2 84.5811767578125, :width 716, :height 1012.6281590388325}, :rects ({:x1 142.9036407470703, :y1 68.60894775390625, :x2 577.541259765625, :y2 84.5811767578125, :width 716, :height 1012.6281590388325}), :page 53}, :content {:text "나중의 벡터 가 이전 단계에 끼어들지 않는 점이 그림-슈미트 과정의 핵심"}, :properties {:color "yellow"}} {:id #uuid "6a82e471-8752-473f-aed8-f6ed247a229c", :page 53, :position {:bounding {:x1 71, :y1 264.99609375, :x2 621, :y2 345.99609375, :width 716, :height 1012.6281590388325}, :rects (), :page 53}, :content {:text "[:span]", :image 1786963056908}, :properties {:color "yellow"}} {:id #uuid "6a82e478-5914-4040-9b53-d8a2f68fc37f", :page 53, :position {:bounding {:x1 208.20310974121094, :y1 497.2005310058594, :x2 353.5611267089844, :y2 514.5616149902344, :width 716, :height 1012.6281590388325}, :rects ({:x1 208.20310974121094, :y1 497.2005310058594, :x2 353.5611267089844, :y2 514.5616149902344, :width 716, :height 1012.6281590388325}), :page 53}, :content {:text "R= QTA는 상삼각행렬"}, :properties {:color "yellow"}} {:id #uuid "6a82e47f-92db-4a59-bdce-d0df63beea35", :page 53, :position {:bounding {:x1 65.7986068725586, :y1 548.2747497558594, :x2 610.64453125, :y2 598.9908752441406, :width 716, :height 1012.6281590388325}, :rects ({:x1 343.6740417480469, :y1 548.2747497558594, :x2 610.64453125, :y2 567.7191467285156, :width 716, :height 1012.6281590388325} {:x1 65.7986068725586, :y1 578.8519592285156, :x2 149.87110900878906, :y2 598.9908752441406, :width 716, :height 1012.6281590388325}), :page 53}, :content {:text "R= QA 의 (i , j ) 성분은 Q'의 행 과 A 의열의 내적이다"}, :properties {:color "yellow"}} {:id #uuid "6a82e487-d001-48ec-b13e-29403412fb4c", :page 53, :position {:bounding {:x1 66.796875, :y1 691.297721862793, :x2 608.6353759765625, :y2 735.8615036010742, :width 716, :height 1012.6281590388325}, :rects ({:x1 254.6766357421875, :y1 691.297721862793, :x2 608.6353759765625, :y2 709.3532638549805, :width 716, :height 1012.6281590388325} {:x1 66.796875, :y1 721.278190612793, :x2 146.88409423828125, :y2 735.8615036010742, :width 716, :height 1012.6281590388325}), :page 53}, :content {:text "A, B , C 의 크기는 각각 √2.√6.√3이며, 이는 R 의 주대각선 위에 있다"}, :properties {:color "yellow"}} {:id #uuid "6a82e48d-f499-42c1-be7f-0d9815a27279", :page 53, :position {:bounding {:x1 66.796875, :y1 786.317253112793, :x2 609.6360473632812, :y2 826.1501388549805, :width 716, :height 1012.6281590388325}, :rects ({:x1 66.796875, :y1 786.317253112793, :x2 609.6360473632812, :y2 799.5117111206055, :width 716, :height 1012.6281590388325} {:x1 66.796875, :y1 812.955680847168, :x2 503.8630676269531, :y2 826.1501388549805, :width 716, :height 1012.6281590388325}), :page 53}, :content {:text "선형독립 인 열을 갖는 모든 행렬 A 는 A= QR 분해를 갖는다 . mx \" 행렬 Q 는 정규직 교하 는열 을 갖는 행렬이고 , 정사각행렬 R은 양 의 주대각성분 을 갖는 상삼각행렬 이다."}, :properties {:color "yellow"}} {:id #uuid "6a82e495-6827-4b31-b48a-8587b88e3771", :page 53, :position {:bounding {:x1 200.26040649414062, :y1 899.2621383666992, :x2 463.36163330078125, :y2 913.150993347168, :width 716, :height 1012.6281590388325}, :rects ({:x1 200.26040649414062, :y1 899.2621383666992, :x2 463.36163330078125, :y2 913.150993347168, :width 716, :height 1012.6281590388325}), :page 53}, :content {:text "ATA = ( QR) TQR =RTQTQR =RTR"}, :properties {:color "yellow"}} {:id #uuid "6a82e4a0-31eb-46da-855f-b75bb5997eb4", :page 54, :position {:bounding {:x1 141.54730224609375, :y1 130.39280700683594, :x2 625.48828125, :y2 148.44834899902344, :width 716, :height 1012.6281590388325}, :rects ({:x1 141.54730224609375, :y1 130.39280700683594, :x2 227.1809844970703, :y2 148.44834899902344, :width 716, :height 1012.6281590388325} {:x1 241.35198974609375, :y1 130.39280700683594, :x2 625.48828125, :y2 148.44834899902344, :width 716, :height 1012.6281590388325}), :page 54}, :content {:text "최소 제곱 문제 RTRE =RTQTb 또는 R² = QTb 또는 i = R -QT6 "}, :properties {:color "yellow"}} {:id #uuid "6a82e4b0-bc89-4b23-8ad5-679bcebd0d64", :page 54, :position {:bounding {:x1 105.95702362060547, :y1 198.8715362548828, :x2 445.9405212402344, :y2 212.7604217529297, :width 716, :height 1012.6281590388325}, :rects ({:x1 105.95702362060547, :y1 198.8715362548828, :x2 445.9405212402344, :y2 212.7604217529297, :width 716, :height 1012.6281590388325}), :page 54}, :content {:text "필요한 계산은 그림- 슈미트 과정에 있는 '번의 곱셈이다."}, :properties {:color "yellow"}} {:id #uuid "6a82e9cf-83c1-44f9-a6df-255f2da97a19", :page 57, :position {:bounding {:x1 42, :y1 51.99609375, :x2 641, :y2 623.99609375, :width 716, :height 1012.6281590388325}, :rects (), :page 57}, :content {:text "[:span]", :image 1786964431525}, :properties {:color "yellow"}} {:id #uuid "6a82ea15-5de9-483d-9c65-15a93c5c3d8a", :page 50, :position {:bounding {:x1 84.69444441795349, :y1 113.77734375, :x2 672.6944444179535, :y2 475.77734375, :width 716, :height 1012.6281590388325}, :rects (), :page 50}, :content {:text "[:span]", :image 1786964500815}, :properties {:color "yellow"}} {:id #uuid "6a82ea1f-56a2-4be1-abac-4cb47a06c55d", :page 48, :position {:bounding {:x1 116.69444441795349, :y1 284.5546875, :x2 651.6944444179535, :y2 323.5546875, :width 716, :height 1012.6281590388325}, :rects (), :page 48}, :content {:text "[:span]", :image 1786964511365}, :properties {:color "yellow"}} {:id #uuid "6a855f6d-02af-464b-ad44-6cdb61f7973c", :page 63, :position {:bounding {:x1 70.73567199707031, :y1 71.23480224609375, :x2 618.9344482421875, :y2 111.77301025390625, :width 716, :height 1012.6281590388325}, :rects ({:x1 168.6089324951172, :y1 71.23480224609375, :x2 618.9344482421875, :y2 85.12368774414062, :width 716, :height 1012.6281590388325} {:x1 70.73567199707031, :y1 97.88412475585938, :x2 214.11473083496094, :y2 111.77301025390625, :width 716, :height 1012.6281590388325}), :page 63}, :content {:text "모든 행렬 A는 유사역행렬 A +를 갖는다. 유사 역행렬은 역행렬 , 좌역행렬 , 우역행렬을 모두 포함 한다."}, :properties {:color "yellow"}} {:id #uuid "6a855f7a-997f-4ca8-95fb-d572477bd8e8", :page 63, :position {:bounding {:x1 59, :y1 115.6640625, :x2 630, :y2 379.6640625, :width 716, :height 1012.6281590388325}, :rects (), :page 63}, :content {:text "[:span]", :image 1787125625873}, :properties {:color "yellow"}} {:id #uuid "6a855fcf-ec62-4b22-a9ec-e7d5d880455e", :page 63, :position {:bounding {:x1 71.66883087158203, :y1 624.3381118774414, :x2 486.26300048828125, :y2 638.9214248657227, :width 716, :height 1012.6281590388325}, :rects ({:x1 71.66883087158203, :y1 624.3381118774414, :x2 486.26300048828125, :y2 638.9214248657227, :width 716, :height 1012.6281590388325}), :page 63}, :content {:text "행렬 A의 랭크 이 <과 <\"을 만족하면 무엇을 기대할 수 있는가 "}, :properties {:color "yellow"}} {:id #uuid "6a855fda-fea7-4d81-972e-04718e48d53c", :page 63, :position {:bounding {:x1 87, :y1 734.38671875, :x2 606, :y2 790.38671875, :width 716, :height 1012.6281590388325}, :rects (), :page 63}, :content {:text "[:span]", :image 1787125722381}, :properties {:color "yellow"}} {:id #uuid "6a855fe0-2eb2-4a14-91bf-9a54a70ea013", :page 63, :position {:bounding {:x1 152.7886199951172, :y1 807.1831512451172, :x2 360.4618835449219, :y2 821.0720062255859, :width 716, :height 1012.6281590388325}, :rects ({:x1 152.7886199951172, :y1 807.1831512451172, :x2 360.4618835449219, :y2 821.0720062255859, :width 716, :height 1012.6281590388325}), :page 63}, :content {:text "2가 영 공간 성분으로 0 을 갖는다"}, :properties {:color "yellow"}} {:id #uuid "6a855ff4-89f2-4e1d-a036-be210e4b63ab", :page 64, :position {:bounding {:x1 82, :y1 468.5234375, :x2 666, :y2 826.5234375, :width 716, :height 1012.6281590388325}, :rects (), :page 64}, :content {:text "[:span]", :image 1787125748462}, :properties {:color "yellow"}} {:id #uuid "6a856002-40c1-44eb-acc5-594e6e5f8c2a", :page 64, :position {:bounding {:x1 110, :y1 255.71875, :x2 643, :y2 295.71875, :width 716, :height 1012.6281590388325}, :rects (), :page 64}, :content {:text "[:span]", :image 1787125762067}, :properties {:color "yellow"}} {:id #uuid "6a85600c-3cac-4ba4-9f76-bc8e55a4ff1c", :page 65, :position {:bounding {:x1 57, :y1 137.6640625, :x2 633, :y2 184.6640625, :width 716, :height 1012.6281590388325}, :rects (), :page 65}, :content {:text "[:span]", :image 1787125772423}, :properties {:color "yellow"}} {:id #uuid "6a85601e-b15a-432c-a104-43aa309f4d34", :page 66, :position {:bounding {:x1 133.4526824951172, :y1 705.3710556030273, :x2 623.96337890625, :y2 719.2599716186523, :width 716, :height 1012.6281590388325}, :rects ({:x1 133.4526824951172, :y1 705.3710556030273, :x2 623.96337890625, :y2 719.2599716186523, :width 716, :height 1012.6281590388325}), :page 66}, :content {:text "행공간 의 두 벡터 z와 X가 열공간의 동일한 벡터 Az= AX 로 갈 수 는 없다는 것"}, :properties {:color "yellow"}} {:id #uuid "6a85602c-bc22-4eb5-86c2-1079716484c5", :page 66, :position {:bounding {:x1 115.62499237060547, :y1 735.0585556030273, :x2 653.9713134765625, :y2 748.9474716186523, :width 716, :height 1012.6281590388325}, :rects ({:x1 115.62499237060547, :y1 735.0585556030273, :x2 653.9713134765625, :y2 748.9474716186523, :width 716, :height 1012.6281590388325}), :page 66}, :content {:text "열공간의 모든 벡터 b= Az는 행 공간 의 단 하나 의 벡터 z 로부터 나온다 . 그러면 A+ b =이다 ."}, :properties {:color "yellow"}} {:id #uuid "6a856034-75b4-4025-8463-6bbce9302041", :page 67, :position {:bounding {:x1 53, :y1 209.5234375, :x2 624, :y2 311.5234375, :width 716, :height 1012.6281590388325}, :rects (), :page 67}, :content {:text "[:span]", :image 1787125811831}, :properties {:color "yellow"}} {:id #uuid "6a85603b-9d37-4456-b37c-0732cb7b80d3", :page 67, :position {:bounding {:x1 68, :y1 458.96875, :x2 622, :y2 500.96875, :width 716, :height 1012.6281590388325}, :rects (), :page 67}, :content {:text "[:span]", :image 1787125818753}, :properties {:color "yellow"}} {:id #uuid "6a856040-be47-4a73-a52b-d486b76c8d2f", :page 67, :position {:bounding {:x1 59, :y1 567.96875, :x2 619, :y2 646.96875, :width 716, :height 1012.6281590388325}, :rects (), :page 67}, :content {:text "[:span]", :image 1787125824274}, :properties {:color "yellow"}} {:id #uuid "6a856047-b418-487d-873c-2967c2407488", :page 67, :position {:bounding {:x1 62, :y1 876.109375, :x2 615, :y2 928.109375, :width 716, :height 1012.6281590388325}, :rects (), :page 67}, :content {:text "[:span]", :image 1787125831688}, :properties {:color "yellow"}} {:id #uuid "6a856065-6171-48c3-88a1-51dd03f8ea10", :page 69, :position {:bounding {:x1 65.28862762451172, :y1 77.11590576171875, :x2 551.5191040039062, :y2 91.0047607421875, :width 716, :height 1012.6281590388325}, :rects ({:x1 65.28862762451172, :y1 77.11590576171875, :x2 551.5191040039062, :y2 91.0047607421875, :width 716, :height 1012.6281590388325}), :page 69}, :content {:text "모든 행렬 A 는 행공간 에서 열 공간 으로(즉 차원에서 차원 으로 )의 가역변환 이다 "}, :properties {:color "yellow"}} {:id #uuid "6a85606a-40c4-4d49-be45-8b3997d0b687", :page 69, :position {:bounding {:x1 55, :y1 103.328125, :x2 616, :y2 209.328125, :width 716, :height 1012.6281590388325}, :rects (), :page 69}, :content {:text "[:span]", :image 1787125866574}, :properties {:color "yellow"}} {:id #uuid "6a856077-68be-4fbd-b9af-716de18b6602", :page 69, :position {:bounding {:x1 67, :y1 504.25, :x2 618, :y2 544.25, :width 716, :height 1012.6281590388325}, :rects (), :page 69}, :content {:text "[:span]", :image 1787125878829}, :properties {:color "yellow"}} {:id #uuid "6a856080-57ec-455d-8096-8c361f5939fc", :page 69, :position {:bounding {:x1 65.28862762451172, :y1 553.1249694824219, :x2 613.1637573242188, :y2 593.5546569824219, :width 716, :height 1012.6281590388325}, :rects ({:x1 65.28862762451172, :y1 553.1249694824219, :x2 613.1637573242188, :y2 567.7082824707031, :width 716, :height 1012.6281590388325} {:x1 66.29773712158203, :y1 579.6658020019531, :x2 241.80441284179688, :y2 593.5546569824219, :width 716, :height 1012.6281590388325}), :page 69}, :content {:text "AT와 AT는 동일한 행공간 과 공간을 갖는다 . 둘 의 차이점은 A + A가 행공간 위로 사영하는대칭인 사영행렬이라는 것이다"}, :properties {:color "yellow"}} {:id #uuid "6a856088-3271-41fd-b568-8a0c1b029b59", :page 69, :position {:bounding {:x1 61, :y1 641.578125, :x2 615, :y2 694.578125, :width 716, :height 1012.6281590388325}, :rects (), :page 69}, :content {:text "[:span]", :image 1787125895702}, :properties {:color "yellow"}}], :extra {:page 72}}