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    Lineare Numerische Analysis

    ISBN-10: 3528082917
    ISBN-13: 9783528082918
    Edition: 0
    Author(s): Noel Gastinel
    Description: Bekanntlich kann man in Rn (oder 0") (d. h. in einem Vektorraum uber R oder 0) eine lineare Abbildung a (im. vorliegenden Kapitel werden wir allgemein diese Schreibweise verwenden) vermittels der zu dieser Transformation gehorenden Matrix A  More...
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    Copyright Year: 0
    Publisher: Vieweg+teubner Verlag
    Publication Date: 1/1/1972
    Binding: Paperback
    Pages: 359
    Size: 7.48" wide x 66.93" long x 96.06" tall
    Weight: 1258.4

    Bekanntlich kann man in Rn (oder 0") (d. h. in einem Vektorraum uber R oder 0) eine lineare Abbildung a (im. vorliegenden Kapitel werden wir allgemein diese Schreibweise verwenden) vermittels der zu dieser Transformation gehorenden Matrix A bezuglich der Fundamentalbasis PlJ = {e* ea **** , en} von Rn definieren. 1 Die i-te Spalte von A ist a(ei). Es sei PlJ' = lei, e*.*.* e~} eine andere Basis von 2 Rn. Einem Vektor entsprechen die Zahlen ~1' ...* ~~, so daB X = ~i ei + ~2 e+ ... + ~~ e~ ist; die 2 Zahlen ~~ sind die Komponenten von X bezuglich der Basis PlJ'. Sie konnen in einer Spalte angeordnet werden, und man erhalt damit den (Spalten-)Vektor Man erkennt sogleich, wie die Komponenten von X' in Abhangigkeit von X zu berechnen sind. Es seien .. e e e e ei = P11 l + P21 a + ... + Pnl n = E Pk1 k, k=l (I) n e~ = PI .. e+ Pan e+ ... + p,." en = E Ph ek 1 a k=l ej = 1; Pkjek). Fur X ergibt sich daraus (oder k=l X = i ~iej = i ~i (i Pklek) = 1; (i Pkj~l) ek = i ~kek.

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