Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T02:24:49.926Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected], [email protected]
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: [email protected], [email protected]
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  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

[1]Chiang, H. and Li, C.K., ‘Linear maps leaving the alternating group invariant’, Linear Algebra Appl. 340 (2002), 69–80.CrossRefGoogle Scholar
[2]Katz, M., ‘On the extreme points of a certain convex polytope’, J. Combinatorial Theory 8 (1970), 417–423.CrossRefGoogle Scholar
[3]Katz, M., ‘On the extreme points of a set of sub-stochastic and symmetric matrices’, J. Math. Anal. Appl. 37 (1972), 576–579.CrossRefGoogle Scholar
[4]Li, C.K., Tam, B.S. and Tsing, N.K., ‘Linear maps preserving permutation and stochastic matrices’, Linear Algebra Appl. 341 (2002), 5–22.CrossRefGoogle Scholar
[5]Lin, S.H. and Tam, B.S., ‘Strong linear preservers of symmetric doubly stochastic or doubly substochastic matrices’, (preprint).Google Scholar