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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Pseudo-similarity for matrices over a field

Authors: R. E. Hartwig and F. J. Hall
Journal: Proc. Amer. Math. Soc. 71 (1978), 6-10
MSC: Primary 15A21
MathSciNet review: 0573006
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Abstract: We call two square matrices A and B (over a ring) pseudo-similar, if matrices $ X,{X^ - },{X^ = }$ exist, such that $ {X^ - }AX = B,XB{X^ = }A,X{X^ - }X = X$ and $ X{X^ = }X = X$. We show that if A and B have the same dimension and if the ring is a field, then pseudo-similarity implies similarity, and hence that pseudo-similarity is an equivalence relation.

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PII: S 0002-9939(1978)0573006-8
Keywords: Pseudo-similarity, inner inverse, matrix equations
Article copyright: © Copyright 1978 American Mathematical Society