Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A21

Retrieve articles in all journals with MSC: 15A21


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0573006-8
PII: S 0002-9939(1978)0573006-8
Keywords: Pseudo-similarity, inner inverse, matrix equations
Article copyright: © Copyright 1978 American Mathematical Society