Pseudo-similarity for matrices over a field
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- by R. E. Hartwig and F. J. Hall
- Proc. Amer. Math. Soc. 71 (1978), 6-10
- DOI: https://doi.org/10.1090/S0002-9939-1978-0573006-8
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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.References
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Bibliographic Information
- © Copyright 1978 American Mathematical Society
- 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