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Canonical Forms for Certain Matrices Under Unitary Congruence

Published online by Cambridge University Press:  20 November 2018

J W. Stander  and
N. A. Wiegmann
J W. Stander
Affiliation:
Catholic University
N. A. Wiegmann
Affiliation:
Washington, D.C.
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If A is a matrix with complex elements and if A = AT (where AT denotes the transpose of A), there exists a non-singular matrix P such that PAPT = D is a diagonal matrix (see (3), for example). It is also true (see the principal result of (5)) that for such an A there exists a unitary matrix U such that UAUT = D is a real diagonal matrix with nonnegative elements which is a canonical form for A relative to the given U, UT transformation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 438 - 446
Copyright
Copyright © Canadian Mathematical Society 1960

References

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