e2867fdecc
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Ufr6wUhJAzBaqcaBiRJ1xk
817 lines
45 KiB
Clojure
Executable File
817 lines
45 KiB
Clojure
Executable File
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:content {:text "두 벡터 가 직교한다는 것은 두 벡터 의 내적 이 0임을 의미한다 ."},
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:content {:text "4가지 기본 부분공간 은 서로 직교하는 관계이다 "},
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:content {:text "식 Az= 0은 2가 행렬 A의 각 행 과 직교 함을 의미하며 , 식 Ay= 0 은 y 가 행렬 A 의 각 열과직교 함을 의미한다"},
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: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."},
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:content {:text "행렬 A의 영공간 은 A의 행공간 과 직교 한다."},
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:content {:text " 의 열공간 C( A) 와 AT 의 영공간 N (AT ) 가 직교한다 "},
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:content {:text "전체 공간 을 구성하는 직교하는 두 부분 공간의 쌍을 특별히 직교여 공간이라 한다"},
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:content {:text "V의 직교 여공간 V- 은V 와 직교 하는 모든 벡터 를 포함 한다."},
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:content {:text "직교 하는 두 부분공간 에 속하는 유일한 벡터는 영벡터이다"},
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:content {:text "해 의 유일성은 해 가 존재 함을 의미 하고, 해 의 존재성은 해가 유일 함을 의미 한다"},
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:content {:text "행렬 A는행공간 에서 열 공간 으로 의 가역변환이다"},
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: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"},
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:content {:text "영공간의 벡터와 행 공간의 벡터 Ay 가 직교 IT( ATy )= (Az)Ty= 0Ty =0"},
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:content {:text "벡터 b 는 S 안에서 가장 가까운 점 p 로 사영된다 . 그러면 오차 벡터 e =b-p 는 부분 공간 S와 직교 한다. "},
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: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"},
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: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."},
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:content {:text "항등행렬 / 에 대해 행렬 - P 도 사영행렬 이어야 한다"},
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:content {:text "P 가 하나의 부분공간 위로 사영 할 때 , I -P 는 그 부분 공간과 직교 하는 부분공간 위로 사영 한다."},
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:content {:text "p = Ai( 사)"},
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: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"},
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:content {:text " ( S) 안에서 벡터 을 구하고 , ( C ) 안에서 사영 p= A²을 구한 다음 , (T) 안에서 사영 행렬 P를 구해보자 ."},
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:content {:text "오차벡터 b - A '은 부분공간 과 직교한다"},
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:content {:text "핵심 은 정규 방정식 (normal equation ) AT ( b- A² )= 0을 해결 하는 단계이다 ."},
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: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 "},
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