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Zur Invariantentheorie

In: Mathematische Werke

Author

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  • Adolf Hurwitz

Abstract

Zusammenfassung Es scheint mir nicht zweckmässig, in der Formentheorie den Begriff der Invariante, wie es zumeist geschieht, von vornherein an die Betrachtung der Formen anzuknüpfen. Denn der Begriff der Invariante hängt gewissermassen nur in indirekter Weise von den Formen ab. Die letzteren dienen nur dazu, die linearen Transformationen der Argumente der Invariante, gegenüber welchen diese die Eigenschaft der Invarianz besitzen soll, zu charakterisieren. Die linearen Transformationen selber bilden das wesentliche Element der Begriffsbildung. Da jede lineare Transformation von nicht verschwindender Determinante sich zerlegen lässt in eine „unimodulare“ (d. h. von der Determinante 1) und in eine Transformation, welche in der Multiplikation aller Variablen mit ein und demselben Faktor besteht, so ist es völlig ausreichend, nur unimodulare Transformationen zu betrachten, so lange man sich auf homogene Funktionen beschränkt.

Suggested Citation

  • Adolf Hurwitz, 1963. "Zur Invariantentheorie," Springer Books, in: Mathematische Werke, chapter 0, pages 508-532, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-4160-3_36
    DOI: 10.1007/978-3-0348-4160-3_36
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