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Grundeigenschaften der Determinanten

In: Vorlesungen über Algebra

Author

Listed:
  • Ludwig Bieberbach

    (Friedrich-Wilhelms-Universität Berlin)

Abstract

Zusammenfassung Die Lehre von den Determinanten knüpft unmittelbar an die Auflösung eines Systems linearer Gleichungen an. Die Resultante eines Systems linearer Gleichungen ist nämlich geradezu die Determinante der Koeffizienten dieses Systems von Gleichungen. Nun lassen sich die Resultanten eines Systems von linearen Gleichungen zwar leicht berechnen. Aber die Elimination von zwei Variablen x, y aus drei linearen Gleichungen führt schon zu einer Resultante von 6 Gliedern; die Resultante von vier linearen Gleichungen mit drei Variablen ist ein Aggregat aus 24 Gliedern; die Resultante aus fünf linearen Gleichungen mit vier Variablen enthält 120 Glieder usf.

Suggested Citation

  • Ludwig Bieberbach, 1928. "Grundeigenschaften der Determinanten," Springer Books, in: Vorlesungen über Algebra, edition 0, chapter 0, pages 41-52, Springer.
    • Handle: RePEc:spr:sprchp:978-3-663-15774-8_6
    DOI: 10.1007/978-3-663-15774-8_6
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