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VII. Skalarprodukt og projektion – 1. Ortogonal projektion 484 Eksempel For et underrum U = span(a) ⊂ Rn udspændt af netop én vektor a = 0 er den ortogonale projektion af en vektor v på U givet ved v · a u = a · a a Det skrives proja(v) = v · a a · a a 1.14. Projektion på vektor ☞ [LA] 12 Ortogonal projektion Eksempel - figur v u = a w = v u ∈ U ⊥ U = span(a)
VII. Skalarprodukt og projektion – 1. Ortogonal projektion 485 Ortogonal projektion u = proja(v) på span(a) λ = v·a a·a 1.15. Projektion på en vektor ☞ [LA] 12 Ortogonal projektion Eksempel - argument For et underrum U = span(a) er er den ortogonale projektion v på U givet ved v · a u = proja(v) = a · a a Eftervis altså (v − (v − v · a a) ⊥ a a · a v · a v · a a) · a = v · a − a · a = 0 a · a a · a 1.16. Projektion på en vektor ☞ [LA] 12 Ortogonal projektion Eksempel For et underrum U = span(a) ⊂ R3 udspændt af vektoren a = (1,1,1) er den ortogonale projektion af en vektor v = (v1,v2,v3) på U givet ved v · a proja(v) = a · a a
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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 - 2. Partielle a
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I. Differentiation - 3. Tangentplan
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I. Differentiation - 4. Kædereglen
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I. Differentiation - 5. Gradient 88
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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 - 2. 1. o
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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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