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A characterization of strong preservers of matrix majorization

โœ Scribed by LeRoy B Beasley; Sang-Gu Lee; You-Ho Lee

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
86 KB
Volume
367
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

A matrix A is said to be matrix majorized by a matrix B, written A โ‰บ B, if there exists an n ร— n row stochastic matrix X such that A = BX. This is a generalization of multivariate majorization.

In this paper, we characterize the linear operators that strongly preserve the matrix majorization.

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Let F be a field. Let V denote the vector space of all m ร— n matrices over F or the vector space of all n ร— n symmetric matrices over F of characteristic not 2 or 3. For each fixed positive integer s 2, let Q s denote the set of all matrix pairs (A, B) in V such that rank(A + B) = rank(A) + rank(B)