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Signature matrix algebras and bipartite graphs

Authors
  • Aguirre Holguín, Valeria
  • Wojciechowski, Piotr J.1, 2, 1, 3
  • 1 Department of Mathematical Sciences
  • 2 New Mexico State University
  • 3 The University of Texas at El Paso
Type
Published Article
Journal
Linear Algebra and its Applications
Publisher
Elsevier
Publication Date
Jan 01, 2014
Accepted Date
Mar 12, 2014
Identifiers
DOI: 10.1016/j.laa.2014.03.016
Source
Elsevier
Keywords
License
Unknown

Abstract

A special class of matrix algebras, the rc-signature algebras, naturally emerged as a result of the study of a Multiplicative Decomposition Property of matrices (a multiplicative analogue of the Riesz Decomposition Property in ordered vector spaces). This note is devoted to the study of a tractable subclass of these algebras. It is proven that a necessary and sufficient condition for two such algebras to be isomorphic is the simultaneous permutation-similarity between the members of the algebras. There is a one-to-one correspondence between the signature algebras and the bipartite graphs that respects the isomorphism between the algebras and the strict isomorphism between the bipartite graphs.

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