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VII. Skalarprodukt og projektion – 1. Ortogonal projektion 482 Komplement - figur (1, 2,1) x z U=span((1,1,1),(2,3,4)) 1.10. Nedfæld vinkelret ☞ [LA] 12 Ortogonal projektion Projektion - figur v u y w = v u ∈ U ⊥ Ortogonal projektion på underrum U
VII. Skalarprodukt og projektion – 1. Ortogonal projektion 483 1.11. Projektion ☞ [LA] 12 Ortogonal projektion Definition For et underrum U ⊂ V = R n er den ortogonale projektion af en vektor v på U den vektor u ∈ U som opfylder v − u = w ∈ U ⊥ Der gælder Den ortogonale projektion betegnes v = u + w, u ∈ U, w ∈ U ⊥ projU(v) = u 1.12. Projektion på koordinatplan ☞ [LA] 12 Ortogonal projektion Eksempel For underrumet U = span(e1,e2) ⊂ R n er den ortogonale projektion af en vektor v = (v1,v2,...,vn) på U givet ved projU(v) = u = (v1,v2,0,...,0) Ses let da v − u = (0,0,v3,...,vn) ∈ U ⊥ 1.13. Projektion på en vektor ☞ [LA] 12 Ortogonal projektion
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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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I. Differentiation - 4. Kædereglen
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I. Differentiation - 6. Maksimum/mi
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I. Differentiation - 7. Lagrangemet
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II. Integration - 1. Dobbelt integr
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II. Integration - 2. Itereret integ
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II. Integration - 3. Generelle omr
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III. Potensrækker - 1. l’Hospita
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III. Potensrækker - 2. Talfølger
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III. Potensrækker - 3. Potensrækk
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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IV. Differentialligninger - 3. Gene
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1. Vektorer og matricer V Matricer
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V. Matricer - 1. Vektorer og matric
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V. Matricer - 2. Lineære afbildnin
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V. Matricer - 3. Lineære ligninger
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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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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etningsafledede, 89, 102 retningsfe
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