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VI. Egenvektorer og diagonalisering – 1. Egenvektorer 436 Definition Lad A være en n × n-matrix. En n-søjlevektor u kaldes en egenvektor for A, hvis for en skalar λ ∈ R. Au = λu Hvis u = 0 kaldes λ en egenværdi for A og u er en egentlig egenvektor. Nulvektoren er altid en egenvektor. 1.3. Vektorer skaleres ☞ [LA] 9 Egenværdier og egenvektorer For en egenvektor gælder u Au ∈ span(u) Au = u
VI. Egenvektorer og diagonalisering – 1. Egenvektorer 437 1.4. Mange egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer Eksempel Identitetsmatricen In opfylder Inu = u for alle vektorer u. Altså er alle vektorer egenvektorer og tallet 1 er eneste egenværdi. 1.5. Mange egenvektorer ☞ [LA] 9 Egenværdier og egenvektorer Eksempel Nulmatricen 0n opfylder 0nu = 0 for alle vektorer u. Altså er alle vektorer egenvektorer og tallet 0 er eneste egenværdi. 1.6. Gættet eksempel ☞ [LA] 9 Egenværdier og egenvektorer Eksempel Matricen har egentlige egenvektorer u1 = e1 = A = −1 0 0 3 1 ,u2 = e2 = 0 0 1
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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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1. Grafiske/numeriske metoder IV Di
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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