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VII. Skalarprodukt og projektion – 1. Ortogonal projektion 490 = a 2 + b 2 1.24. Pythagoras ☞ [LA] 12 Ortogonal projektion Pythagoras - figur Pythagoras som du kender den a + b a b a 2 + b 2 = a + b 2 1.25. Afstand til underrum ☞ [LA] 12 Ortogonal projektion Sætning 19 Lad U ⊂ V = R n vœre et underrum. Antag at vektoren v har ortogonal projektion u på U. Så er u den vektor i U, der har kortest afstand til v.
VII. Skalarprodukt og projektion – 1. Ortogonal projektion 491 Bevis For en vektor u − u ′ ∈ U gælder v − (u − u ′ ) 2 = (v − u) + u ′ 2 i følge Pythagoras, Sætning 18, da (v − u) ⊥ u ′ . = v − u 2 + u ′ 2 1.26. Mindste afstand ☞ [LA] 12 Ortogonal projektion Sætning 19 - figur v v u u u ′ Mindste afstand til underrum v (u u ′ ) 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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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 - 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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II. Integration - 4. Koordinatskift
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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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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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etningsafledede, 89, 102 retningsfe
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