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VI. Egenvektorer og diagonalisering – 1. Egenvektorer 450 For λ3 = 2 er koefficientmatricen ⎛ −1 0 ⎞ 1 ⎛ 1 0 ⎞ −1 A − 2I = ⎝ 0 −1 1 ⎠ ∼ ⎝0 1 −1⎠ 2 −1 −1 0 0 0 Heraf fås egenvektorerne ⎛ hvor x3 vælges frit. ⎝ x1 x2 x3 ⎞ ⎛ ⎠ = ⎝ x3 x3 x3 ⎞ ⎛ ⎞ 1 ⎠ = x3 ⎝1⎠ 1 1.30. Egenrum ☞ [LA] 9 Egenværdier og egenvektorer Eksempel 3, 4 - fortsat ⎛ 1 0 ⎞ 1 A = ⎝0 1 1⎠ 2 −1 1 har egenværdier λ1 = 0, λ2 = 1, λ3 = 2 og egenrum ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ 1 −1 2 1 E0 = span{ ⎝−1⎠}, E1 = span{ ⎝1⎠}, E2 = span{ ⎝1⎠} 1 0 1 1.31. Egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer
VI. Egenvektorer og diagonalisering – 1. Egenvektorer 451 Eksempel 3, 4 - figur x ( 1, 1,1) z (1,1,1) (0.5,1,0) Egenvektorer 1.32. Tredjegradsligning ☞ [LA] 9 Egenværdier og egenvektorer Eksempel 7 1 − λ 0 0 0 −λ 1 0 1 = (1 − λ) −λ −λ 1 1 −λ = −(1 − λ) 2 (1 + λ) y
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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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1. Grafiske/numeriske metoder IV Di
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Litteratur • Arnold, Ordinary dif
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