Canonical Forms for Unitary Congruence and *Congruence

Details Canonical Forms for Unitary Congruence and *Congruence Canonical Forms for Unitary Congruence and *Congruence

2007-10-08

arxiv.org/abs/0710.1530v1

Mathematics

Representation Theory

43 pages, to be published in Linear Multilinear Algebra

Scientific paper

We use methods of the general theory of congruence and *congruence for complex matrices--regularization and cosquares--to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that \bar{A}A (respectively, A^2) is normal. As special cases of our canonical forms, we obtain--in a coherent and systematic way--known canonical forms for conjugate normal, congruence normal, coninvolutory, involutory, projection, and unitary matrices. But we also obtain canonical forms for matrices whose squares are Hermitian or normal, and other cases that do not seem to have been investigated previously. We show that the classification problems under (a) unitary *congruence when A^3 is normal, and (b) unitary congruence when A\bar{A}A is normal, are both unitarily wild, so there is no reasonable hope that a simple solution to them can be found.

Affiliated with

Also associated with

No associations

Rating

Canonical Forms for Unitary Congruence and *Congruence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Canonical Forms for Unitary Congruence and *Congruence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Canonical Forms for Unitary Congruence and *Congruence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-544309