Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T16:50:27.867Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Choi, M.D., Positive linear maps, Proc. Symp. in Pure Math., 38(II) (1982), pp. 583–590.Google Scholar
2. Helton, J.W. and Rodman, L., Signature preserving linear maps on hermitian matrices, submitted.Google Scholar
3. Marshall, A. and Olkin, I., Inequalities: The Theory of Majorization and its Applications, Academic Press, 1979.Google Scholar
4. Schneider, H., Positive operators and an inertia theorem, Numer. Math., 7 (1965), pp. 11–17.Google Scholar