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Orthogonale Transformation

In: Matrizen

Author

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  • Rudolf Zurmühl

Abstract

Zusammenfassung Ein bedeutsamer Sonderfall linearer Transformationen liegt in jener affinen Verzerrung bzw. Koordinatentransformation vor, die sich im dreidimensionalen Falle als eine reine Drehung darstellt. Obgleich es sich hier nicht um eine „Verzerrung“ im landläufigen Sinne handelt, wird doch auch die Drehung durch eine Lineartransformation in der Form y = Cx wobei freilich die Matrix ganz bestimmte Eigenschaften aufweist. Die charakteristische Eigenschaft dieser Linear-transformation, daß ein System rechtwinkliger (orthogonaler) Einheits-vektoren in ein ebensolches System übergeführt wird, führt zur n-dimensionalen Verallgemeinerung, den sogenannten orthogonalen Transformationen gemäß der folgenden

Suggested Citation

  • Rudolf Zurmühl, 1950. "Orthogonale Transformation," Springer Books, in: Matrizen, chapter 7, pages 50-57, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-53289-4_7
    DOI: 10.1007/978-3-642-53289-4_7
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