Linear operators preserving certain functions on singular values of matrices |
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| Authors: | Chi-Kwong Li Nam-Kiu Tsing |
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| Institution: | 1. Department of Mathematics , The College of William and Mary , Williamsburg, Virginia, 23185;2. Systems Research Center and Electrical Engineering Department , University of Maryland , aryland, College Park, 20742 |
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| Abstract: | We study the structure of those linear operators on the rectangular complex or real matrix spaces that preserve certain functions on singular values. We first do a brief survey on the existing results in the area and then prove a theorem which covers and extends all of them. In particular. our theorem confirms two conjectures about the structure of those linear operators preserving the completely symmetric functions on powers of singular values of matrices. |
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