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V. Matricer – 1. Vektorer og matricer 384 ⎛ 1 0 ⎞ 0 I3 = ⎝0 1 0⎠ 0 0 1 1.32. Multiplikation af identitetsmatrix ☞ [LA] 2 Matricer Sætning 3 Lad A vœre en m × n-matrix. Så gœlder ImA = A = AIn "Matrix multiplikation med identitetsmatricen œndrer ikke en matrix." Bevis Den j-te søjle i In er ej, så den j-te søjle i AIn er den j-te søjle i A. Aej = a •j
V. Matricer – 2. Lineære afbildninger 385 2. Lineære afbildninger 2.1. Oversigt ☞ [LA] 3, 4, 5 Nøgleord og begreber ✌ Fra matrix til afbildning ✌ Fra afbildning til matrix ✌ Test matrix-afbildning ✌ Inverse matricer ✌ Test invers matrix ✌ Matrix potens ✌ Lineære ligningssystemer ✌ Løsningsmængdens struktur ✌ Test løsningsmængde 2.2. Lineær afbildning ☞ [LA] 3 Lineære funktioner Definition f : R n → R m er en lineær afbildning, hvis linearkombinationer bevares f(λ1u1 + · · · + λkuk) = λ1f(u1) + · · · + λkf(uk)
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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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I. Differentiation - 1. Kontinuitet
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I. Differentiation - 4. Kædereglen
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I. Differentiation - 7. Lagrangemet
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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1. Egenvektorer VI Egenvektorer og
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VI. Egenvektorer og diagonalisering
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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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