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VII. Skalarprodukt og projektion – 1. Ortogonal projektion 480 1.6. Komplement ☞ [LA] 11 Skalarprodukt i R n Komplement - figur span(u) ⊥ ( 1 3 ,1) y 1 u = (3,1) 1.7. Tømrersvend ☞ [LA] 11 Skalarprodukt i R n Sætning (tømrerprincippet) x
VII. Skalarprodukt og projektion – 1. Ortogonal projektion 481 For en delmængde af vektorer X ⊂ V = R n som udspænder et underrum U ⊂ V er det ortogonale komplement X ⊥ = U ⊥ Altså gælder w ⊥ U ⇔ w ⊥ x, ∀x ∈ X 1.8. Komplement ☞ [LA] 11 Skalarprodukt i R n Komplement - eksempel For U = span((1,1,1),(2,3,4)) ⊂ R 3 er det ortogonale komplement U ⊥ = {v|v · u = 0, ∀u ∈ U} bestemt ved ligningssystemet, v = (v1,v2,v3), v1 + v2 + v3 = 0 2v1 + 3v2 + 4v3 = 0 Løsning ⎛ ⎝ v1 v2 v3 ⎞ ⎛ ⎞ ⎛ ⎞ v3 1 ⎠ = ⎝−2v3⎠ = v3 ⎝−2⎠ 1 v3 1.9. Komplement ☞ [LA] 11 Skalarprodukt i R n
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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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1. Vektorer og matricer V Matricer
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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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