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VII. Skalarprodukt og projektion – 1. Ortogonal projektion 478 1.2. Prikprodukt ☞ [LA] 11 Skalarprodukt i Rn Definition For vektorer a = (a1,...,an),b = (b1,...,bn) i Rn er skalarproduktet n a · b = og lœngden, normen og afstanden mellem vektorer a og b i=1 aibi a = √ a · a a − b 1.3. Vinkelret ☞ [LA] 11 Skalarprodukt i R n Definition b a Vinkerette vektorer To vektorer a,b i R n er ortogonale, vinkelrette, hvis a · b = 0. Det skrives også a ⊥ b ⇔ a · b = 0
VII. Skalarprodukt og projektion – 1. Ortogonal projektion 479 1.4. Komplement ☞ [LA] 11 Skalarprodukt i R n Definition For en delmængde af vektorer X ⊂ V = R n er det ortogonale komplement underrummet Der gælder X ⊥ = {v|v · u = 0, ∀u ∈ X} 0 ⊥ = V, V ⊥ = 0 1.5. Komplement ☞ [LA] 11 Skalarprodukt i R n Komplement - eksempel For u = (3,1) ∈ R 2 er det ortogonale komplement bestemt ved ligningen, v = (v1,v2), Løsning v1 = v2 {v|v · u = 0} 3v1 + v2 = 0 1 −3 v2 = v2 v2 1 −3 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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I. Differentiation - 1. Kontinuitet
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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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