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Linear maps leaving invariant subsets of nonnegative symmetric matrices

Published online by Cambridge University Press:  17 April 2009

Hanley Chiang  and
Chi-Kwong Li
Hanley Chiang
Affiliation:
Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187-8795, United States of America, e-mail: hschia@wmalumni.com, ckli@math.wm.edu
Chi-Kwong Li
Affiliation:
Department of Mathematics, College of William and Mary, P.O.Box 8795, Williamsburg, VA 23187-8795, United States of America, e-mail: hschia@wmalumni.com, ckli@math.wm.edu
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Abstract

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Let  be a certain set of nonnegative symmetric matrices, such as the set of symmetric doubly stochastic matrices or the set, of symmetric permutation matrices. It is proven that a linear transformation mapping  onto  must be of the form X ↦ PtX P for some permutation matrix P except for several low dimensional cases.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 221 - 231
Copyright
Copyright © Australian Mathematical Society 2003

References

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