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Matrizentheorie by Felix R. Gantmacher, H. Boseck, K. Stengert

Matrizentheorie

by Felix R. Gantmacher , H. Boseck , K. Stengert
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Book cover type: Paperback
  • ISBN13: 9783642712449
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 654
  • Original Price: EUR 56.07
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 1035 grams
  • BISAC Subject(s): Algebra / General

12.1. 1. In diesem Kapitel wird folgende Frage behandelt: Gegeben seien vier Matnzen A, B, A1, B1 gleichen Typs (m, n) mit Elementen aus e nem Zahlkorper K. Gesucht s nd die Bedingungen, unter denen zwei regulare quadra- t 8che Matrizen P und Q der Ordnung m bzw. n existieren derart, dafJ gleichzeitig (1) giU. 1) Fuhrt man die Matrizenbuschel A + J..B und A1 + J..B ein, so k6nnen die beiden 1 Matrizengleichungen (1) durch die einzige Gleichung (2) P(A + J..B) Q = A1 + J..B1 ersetzt werden. Definition 1. Wir nennen zwei Buschel A + J..B und A1 + J..B rechteckiger Ma- 1 trizen gleichen Typs (m, n) streng aquivalent, wenn fUr sie die Gleichung (2) gilt und dabei P und Q konstante (d. h. von J.. unabhiingige) regulare quadratische Matrizen 2 (m-ter bzw. n-ter Ordnung) sind. ) Nach der allgemeinen Definition, der Aquivalenz von Polynommatrizen (vgl.

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