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Linear Maps on Hermitian Matrices: The Stabilizer of an Inertia Class

Published online by Cambridge University Press:  20 November 2018

Charles R. Johnson  and
Stephen Pierce
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Abstract

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Let T be a linear transformation acting on the space of n x n complex matrices. Let G(k) be the set of all hermitian matrices with k positive and n — k negative eigenvalues. Let T map some indefinite inertia class G(k) onto itself. We classify all such T. The possibilities are congruence, congruence followed by transposition, and, if n = 2k, it is possible that — T can be a congruence or a congruence followed by transposing. In other words, negation is an admissible transformation when n = 2k.

Keywords

Hermitian matrixinertia class15A2115A27
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 401 - 404
Copyright
Copyright © Canadian Mathematical Society 1985

References

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