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Simultaneous Unitary Invariants for Sets of Matrices

Published online by Cambridge University Press:  20 November 2018

Heydar Radjavi
Heydar Radjavi*
Affiliation:
University of Minnesota, Minneapolis, Minnesota; University of Toronto, Toronto, Ontario
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It is our aim in this paper to give an elementary solution to the problem of simultaneous unitary equivalence of two finite sets of matrices, i.e., given two ordered sets {Aj} and {Bj} of n × n matrices, j = 1, 2, … , m, we wish to determine whether there exists a unitary matrix U such that Bj = U*AjU for all j. A special case of this problem is that of unitary equivalence of two arbitrary matrices.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1012 - 1019
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This paper is based on part of the work done under the supervision of Professor Gerhard K. Kalisch and supported by the National Science Foundation under grant G 14137.

References

1. Brenner, J., The problem of unitary equivalence, Acta Math. 86 (1951), 297–308.Google Scholar
2. Littlewood, D. E., On unitary equivalence, J. London Math. Soc. 28 (1953), 314–322.Google Scholar
3. Mitchell, B. E., Unitary transformations, Can. J. Math. 6 (1954), 69–72.Google Scholar
4. Radjavi, Heydar, On unitary equivalence of arbitrary matrices, Trans. Amer. Math. Soc. 104 1962), 363–373.Google Scholar