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ORDER PRESERVING MAPS ON HERMITIAN MATRICES

Part of: Special matrices

Published online by Cambridge University Press:  07 June 2013

PETER ŠEMRL  and
AHMED RAMZI SOUROUR
PETER ŠEMRL*
Affiliation:
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000, Slovenia
AHMED RAMZI SOUROUR
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8P 5C2 email sourour@uvic.ca
*
✉peter.semrl@fmf.uni-lj.si
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Abstract

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We prove that a continuous map $\phi $ defined on the set of all $n\times n$ Hermitian matrices preserving order in both directions is up to a translation a congruence transformation or a congruence transformation composed with the transposition.

Keywords

order preserving mapHermitian matrix

MSC classification

Secondary: 15B48: Positive matrices and their generalizations; cones of matrices 15B57: Hermitian, skew-Hermitian, and related matrices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 1 , August 2013 , pp. 129 - 132
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

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