The Rao-Mitra-Bhimasankaram relation is strongly antisymmetric

IF 1 3区 数学 Q1 MATHEMATICS
Oskar Maria Baksalary , Dennis Bernstein
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引用次数: 0

Abstract

For n×m complex matrices A and B, the Rao-Mitra-Bhimasankaram (RMB) relation RMB, defined by ARMBB if AAA=ABA, is reflexive and antisymmetric, but not transitive. This paper shows that, despite the lack of transitivity, RMB is strongly antisymmetric in the sense that, for all integers n2, A1RMBRMBAnRMBA1 implies A1==An. The proof of this result is based on a novel proof that RMB is antisymmetric.
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来源期刊
CiteScore
2.20
自引率
9.10%
发文量
333
审稿时长
13.8 months
期刊介绍: Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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