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VII. Skalarprodukt og projektion – 1. Ortogonal projektion 494 = −4 5 (1,1, −1, −1) + 4 2 (0,1,1,0) = (−1, 3 7 2 , 2 ,1) 1.31. Opgave ☞ Matematik Alfa 1, August 2002 Opgave 6 - ekstra Restvektoren v − u = (1,2,3,4) − (−1, 3 7 2 , 2 ,1) = (2, 1 2 , −1 2 ,3) har længde, som angiver den mindste afstand fra v til U ||v − u|| = ||(2, 1 2 27 = 2 = 3√ 6 2 , −1 2 ,3)|| 1.32. Tømrermester ☞ [LA] 12.2 Projektion på 2-dim. underrum Tømrermester - figur
VII. Skalarprodukt og projektion – 1. Ortogonal projektion 495 w = v proju(v) v proju(v) To vektorer rettet op 1.33. Tømrermester ☞ [LA] 12.2 Projektion på 2-dim. underrum Bemærkning Lad u,v være ikke-parallelle vektorer der udspænder underrummet U. Sæt v · u w = v − proju(v) = v − u · u u Så er u,w ortogonale og udspænder U. Den ortogonale projektion af vektoren x på U er da projU(x) = proju(x) + projw(x) = x · u x · w u + u · u w · w w u
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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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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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VI. Egenvektorer og diagonalisering
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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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