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
DOI:
https://doi.org/10.1090/S0002-9939-1978-0573006-8
MathSciNet review:
0573006
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Abstract | References | Similar Articles | Additional Information
Abstract: We call two square matrices A and B (over a ring) pseudo-similar, if matrices exist, such that
and
. 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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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1978-0573006-8
Keywords:
Pseudo-similarity,
inner inverse,
matrix equations
Article copyright:
© Copyright 1978
American Mathematical Society