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Logseq/Major Study/assets/5장_행렬식_1788006854821_0.edn

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:content {:text "두 행 을 교환하면 행렬식의 부호가 바뀐다 (두 열 을교환 하는 경우도 마찬가지이다)"},
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:content {:text "detA = 0 은 행렬 A 의 열 들이 선형 독립이 아님 을 의미 한다 "},
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:content {:text "모든 치환행렬의 행렬식은 1 또는 -1이다"},
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:content {:text "행 교환 은 detA에 -1 을 곱하는 것"},
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:content {:text "행렬 A 의 행렬식이 각 행에 대해 선형 적이라는 것이다 "},
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:content {:text "식 ( 2 )에는 또 하나 의 ' 수수께끼 같은 -1 (음수 부호) '이 있다."},
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:content {:text "이때 행렬 A= le 의 여인 수는 d여인수행렬( colactor matrix ) C=1-6-8 ] 안에 있다"},
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:content {:text "놀라운 사실 은 A 와 CT의 곱은 detAb와의 곱 과 같다는 것이다."},
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:content {:text "행렬 CT 는 detA 로 나누어( CT안의 크기 ( n-1 ) 인 여인 수)야 한다. 역행렬 A- '의 모든 성분은 두 행렬식의 비율 , 즉 ( 크기 인 detA) detA 이다"},
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:content {:text "행렬식이 1인 경우 이다 . 따라서 A- '는 정확히 CT = 수반 행렬 (adjugate matrix )"},
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:content {:text "모든 \"에 대해 detA =\"+1 "},
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:content {:text "가역 행렬 A는 detA≠ 0 "},
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:content {:text "특이행렬 A는 detA =0"},
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:content {:text "Aziz에서 고 윳값 와 고유 벡터 는 고 윳값 방정식( AI)z=0 을 만족한다 . 즉 A- J가 특이행렬 이고 det(AI ) = 0 "},
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:content {:text "행렬 이 삼각행렬 이나 대각 행렬 이라면, 다음 과 같이 단순히 주대각성 분들 을 곱함으로써 행렬식을 계산"},
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:content {:text "직교행렬 Q 의 행렬식은 1 또는 -1 이다."},
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:content {:text "A = LU 이면 detA= ( detZ ) (detU )=detU 이다 . 삼각행렬 U 의 행렬식은 피벗들의 곱"},
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:content {:text "PA = LU이면 행 교환이 존재하므로 det=1 또는 -1 이다(치환행렬"},
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:content {:text "행렬 A 의 두 행이 동일하면 A의 행렬식 은0이다"},
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:content {:text "j행에서 행 에 d를 곱한 것을 빼도 detA는 변하지 않는다"},
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:content {:text "( 행 교환이 없는 ) 소거 과정 은 행렬식을 바꾸지 않고 A를간단한 형태로 만든다"},
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:content {:text "항등행렬 / 1 열을 로 바꾼다 . 이렇게 바꾼 삼각 행렬 M 의 행렬식 은 이다. M 에 행렬 A 를 곱하면 1열 은 Ar 가 되고,가정에 따라 Ax= b이다 . B. 의 나머지 열 은 행렬 A 와 동일 하다."},
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:content {:text "크레이머 규칙 에서 각 B 의 행렬식은 행렬 A의 여인이다."},
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:content {:text "A- '는 행렬 A의 여인 들을 포함한다 "},
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:content {:text "( A)= detAB det B가 앞서 살펴본 성질 2. 2. 2 을 만족함을 보이고자 한다"},
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:content {:text "마지막 4 개의 행렬식의 값은 각각 4. -c . -b , a 이다(이들은 모두 여인 수이다) "},
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