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Congruence

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Book cover The Theory of Matrices

Part of the book series: Ergebnisse der Mathematik und Ihrer Grenƶgebiete ((MATHE1,volume 5))

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Abstract

Matrices with elements in a principal ideal ring. If A = P T BP where each matrix has elements in a principal ideal ring V, and if P is unimodular, then A is congruent with B, written \(A\underline{\underline c} B\) Congruence is an instance of equivalence, and is determinative, reflexive, symmetric, and transitive. (Cf. § 22.)

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Authors
  1. C. C. Mac Duffee
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© 1933 Springer-Verlag Berlin Heidelberg

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Mac Duffee, C.C. (1933). Congruence. In: The Theory of Matrices. Ergebnisse der Mathematik und Ihrer Grenƶgebiete, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-99234-6_5

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  • DOI: https://doi.org/10.1007/978-3-642-99234-6_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-98421-1

  • Online ISBN: 978-3-642-99234-6

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