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Skalarprodukte

In: Lineare Algebra

Author

Listed:
  • Albrecht Beutelspacher

    (Justus-Liebig-Universität Gießen, Mathematisches Institut)

Abstract

Zusammenfassung In diesem Kapitel beschäftigen wir uns mit den möglichen (und sinnvollen) Verhältnissen, die zwei Vektoren miteinander haben können. Eine geometrische Betrachtungsweise ist der Winkel, den zwei Vektoren einschlieBen. Wir betrachten in diesem Kapitel nur solche Ver-hältnisse von Vektoren, die sich durch ein Korperelement beschreiben lassen. Mit anderen Worten: Wir betrachten also Abbildungen von VxV in K; solche Abbildungen nennt man traditionell Formen. Unglücklicherweise gibt es einen ganzen Zoo von verschiedenen und zu unterscheidenden Formen. Ich versuche, Ihnen dadurch Orientierung zu verschaffen, daß ich Ihnen zunächst nur eine Hälfte dieses Zoos zeige, nämlich denjenigen Teil, dessen Ziel das Studium der Skalarprodukte in reellen Vektorräumen ist. Sie sind eingeladen, die paral-lele Theorie für Skalarprodukte in komplexen Vektorraumen im „Projekt“ dieses Kapitels zu entwickeln.

Suggested Citation

  • Albrecht Beutelspacher, 2001. "Skalarprodukte," Springer Books, in: Lineare Algebra, edition 5, chapter 10, pages 245-278, Springer.
    • Handle: RePEc:spr:sprchp:978-3-322-92846-7_10
    DOI: 10.1007/978-3-322-92846-7_10
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