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A Unitary Relation Between a Matrix and its Transpose

Published online by Cambridge University Press:  20 November 2018

William R. Gordon
William R. Gordon*
Affiliation:
University of Victoria, Victoria, British Columbia
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It is well known that if A is an n × n complex matrix and AT is its transpose, then there is an invertible n x n complex matrix S such that AT = S-1AS. In this note we wish to point out another simple relation between A and AT.

If A is an n × n complex matrix and AT is its transpose then there are unitary n × n complex matrices U and V such that AT = UAV.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 2 , June 1970 , pp. 279 - 280
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Eckart, C. and Young, G., A principal axis transformation for non-hermitian matrices. Bull. Amer. Math. Soc. 45 (1939), 118-121.Google Scholar