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VI. Egenvektorer og diagonalisering – 2. Diagonalisering 456 ✌ Længde 2.2. Enhedsvektorer Eksempel ☞ [LA] 3 Lineære funktioner Den i-te standard enhedsvektor ei er (søjle,række)-vektoren, hvis i-te koordinat er 1 og alle øvrige er 0. ⎛ ⎞ 0 ⎜ . ⎟ ⎜ . ⎟ ei = ⎜ ⎜1 ⎟ ⎜ . ⎟ ⎝ . ⎠ 0 ei = 0, ..., 1, ..., 0 2.3. Multiplikation af enhedsvektorer ☞ [LA] 2 Matricer Eksempel - fortsat Den i-te standard enhedsvektor ei multiplicerer fra højre som søjle og fra venstre som række. For en m × n-matrix A er produktet den j-te søjle i A Aej = a •j
VI. Egenvektorer og diagonalisering – 2. Diagonalisering 457 og produktet den i-te række i A. eiA = ai• 2.4. Kvadratisk matrix, identitetsmatrix ☞ [LA] 2 Matricer Definition En kvadratisk n-matrix er en n × n-matrix. En diagonalmatrix er en kvadratisk matrix, hvor indgange udenfor diagonalen alle er 0. Identitetsmatricen (enhedsmatricen) ⎛ 1 0 ⎞ ... ⎜ In = ⎜ ⎝ 0 . . .. 0 ⎟ 0 ⎟ ⎠ 1 med 1 i diagonalen og 0 udenfor er en diagonalmatrix. 2.5. Multiplikation af identitetsmatrix ☞ [LA] 2 Matricer Sætning 3 Lad A vœre en m × n-matrix. Så gœlder ImA = A = AIn "Matrix multiplikation med identitetsmatricen œndrer ikke en matrix."
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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