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VI. Egenvektorer og diagonalisering – 2. Diagonalisering 474 Bemærkning For en vektor a = (a1,...,an) er længden En vektor med længde kaldes en enhedsvektor a = a 2 1 + · · · + a2 n a = 1 2.38. Skalarprodukt udregnet ☞ [S] 9.3 The dot product Eksempel Vektorerne a = (1,3,4,1) og b = (−2,0,2,5) har prikprodukt og længder a · b = 1 · (−2) + 3 · 0 + 4 · 2 + 1 · 5 = 11 a = √ a · a = √ 27 b = √ b · b = √ 33 2.39. Enhedsvektor i given retning ☞ [S] 9.3 The dot product Eksempel
VI. Egenvektorer og diagonalisering – 2. Diagonalisering 475 Vektoren a = (1,3,4,1) har længde Enhedsvektoren i a’s retning er a = √ a · a = √ 27 a 1 = ( √ , a 27 3 √ , 27 4 √ , 27 1 √ ) 27 2.40. Skalarprodukt, regneregler ☞ [LA] 11 Skalarprodukt i R n Regneregler for skalarprodukt (a,b) ↦→ a · b (1) a · a = a 2 ≥ 0 (2) a · b = b · a (3) a · (b + c) = a · b + a · c (4) a · (λb) = λ(a · b) (5) a · a = 0 ⇔ a = 0
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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1. Grafiske/numeriske metoder IV Di
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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