Linear maps preserving Pareto eigenvalues

Abstract

In this paper, we give the characterization of Pareto eigenvalues preserving linear maps on real square matrices. In fact, we show that a linear map on , the algebra of all n by n matrices with real entries, preserves Pareto eigenvalues if and only if , for some nonnegative generalized permutation matrix P.

Keywords:

• Linear preservers
• Pareto eigenvalues

AMS Subject Classifications:

• 15A86
• 90C33

Acknowledgements

The authors are very grateful to the reviewer for carefully reading the paper and for his (her) constructive comments and suggestions which have improved the paper.

Notes

No potential conflict of interest was reported by the authors.