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VI. Egenvektorer og diagonalisering – 1. Egenvektorer 454 Heraf fås egenvektorerne ⎛ hvor x1,x3 vælges frit. ⎝ x1 x2 x3 ⎞ ⎛ ⎠ = ⎝ x1 x3 x3 ⎞ ⎛ ⎞ 1 ⎛ ⎞ 0 ⎠ = x1 ⎝0⎠ + x3 ⎝1⎠ 0 1 1.37. Egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer Eksempel 7 - figur x (0, 1,1) z (1,0,0) Egenvektorer (0,1,1) 1.38. Egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer y
VI. Egenvektorer og diagonalisering – 2. Diagonalisering 455 Eksempel 7 - fortsat For λ1 = −1 er egenrummet For λ2 = 1 er egenrummet 2. Diagonalisering ⎛ ⎞ 0 E−1 = span{ ⎝−1⎠} 1 ⎛ ⎞ ⎛ ⎞ 1 0 E1 = span{ ⎝0⎠ , ⎝1⎠} 0 1 2.1. Oversigt ☞ [LA] 10, 11; [S] 9.3 Nøgleord og begreber ✌ Repetition: enhedsvektor og identitetsmatrix ✌ Diagonalmatricer ✌ Diagonalisering og egenvektorer ✌ Matrixpotens ✌ August 2002, opgave 2 ✌ Skalarprodukt
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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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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. Vektorer og matricer V Matricer
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V. Matricer - 1. Vektorer og matric
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IX. Opgaver - 1. August 2002 524 1.
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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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etningsafledede, 89, 102 retningsfe
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