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V. Matricer – 1. Vektorer og matricer 372 1.10. Span ☞ [LA] 1 Koordinatvektorer Definition Givet et sæt af vektorer u1,...,uk i R n . Så er deres span alle linearkombinationer v = λ1u1 + · · · + λkuk Et span er stabilt overfor dannelse af linearkombination og giver et underrum af R n . Eksempel Diagonalen i talplanen er et span {(x,y)|x = y} = span((1,1)) ⊂ R 2 1.11. Vektorrum ☞ [LA] 1 Koordinatvektorer, [S] 9.2 Vectors Definition En mængde med struktur som et koordinatvektorrum kaldes et vektorrum og elementerne kaldes vektorer. Vektorer kan adderes og skalarmultipliceres med reelle skalarer. Eksempel Et underrum i R n er et vektorrum. Eksempel
V. Matricer – 1. Vektorer og matricer 373 Mængden af alle reelle funktioner f : X → R er et vektorrum. 1.12. Test linearkombination ☞ [LA] 1 Koordinatvektorer Test Enhver vektor x ∈ R 3 kan skrives som en linearkombination x = λ1(1,1, −1) + λ2(−1, −1,1). Løsning som alle har samme 1. og 2. koordinat. x = λ1(1,1, −1) + λ2(−1, −1,1) = (λ1 − λ2)(1,1, −1) Afkryds: ja nej 1.13. Matrix indgang ☞ [LA] 2 Matricer Definition En m × n-matrix er et rektangulært regneark med m-rækker og n-søjler. Det skrives (A = A) ij-te (matrix)indgang A = (aij)i=1...m,j=1...n ⎛ ⎞ = ⎜ ⎝ a11 ... a1n . aij . am1 ... amn aij ⎟ ⎠
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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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V. Matricer - 4. Determinanter = (
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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