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V. Matricer – 2. Lineære afbildninger 392 = AInA −1 = AA −1 = In 2.13. Test invers matrix ☞ [LA] 4 Inverse matricer Test Lad A,B være invertible n × n-matricer. Så gælder (AB) −1 = A −1 B −1 . Løsning Den rigtige formel er (AB) −1 = B −1 A −1 Afkryds: ja nej 2.14. Matrix potens ☞ [LA] 2 Matricer Definition For en kvadratisk n × n-matrix A defineres potens, k = 0,1,2,..., Hvis A er invertibel, så er A 0 = In, A k = A k−1 A A −k = (A −1 ) k = (A k ) −1
V. Matricer – 2. Lineære afbildninger 393 For enhedsmatricen er In k = In 2.15. Pas på matrix potens ☞ [LA] 2 Matricer Bemærkning Potensregneregler gælder A l A m = A l+m Men normalt er For eksempel (A l ) m = A lm A m B m = (AB) m A 2 B 2 = (AA)(BB) = (AB)(AB) = (AB) 2 2.16. Potens af diagonalmatrix Eksempel ☞ [LA] 2 Matricer For en diagonal n × n-matrix ⎛ ⎞ Λ = λ1 0 ... . 0 .. ⎟ 0 ⎟ ⎠ . 0 λn ⎜ ⎝
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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