Linear Preservers of Perimeters of Nonnegative Real Matrices

- Journal title : Kyungpook mathematical journal
- Volume 48, Issue 3, 2008, pp.465-472
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2008.48.3.465

Title & Authors

Linear Preservers of Perimeters of Nonnegative Real Matrices

Song, Seok-Zun; Kang, Kyung-Tae;

Song, Seok-Zun; Kang, Kyung-Tae;

Abstract

For a nonnegative real matrix A of rank 1, A can be factored as for some vectors a and b. The perimeter of A is the number of nonzero entries in both a and b. If B is a matrix of rank k, then B is the sum of k matrices of rank 1. The perimeter of B is the minimum of the sums of perimeters of k matrices of rank 1, where the minimum is taken over all possible rank-1 decompositions of B. In this paper, we obtain characterizations of the linear operators which preserve perimeters 2 and k for some . That is, a linear operator T preserves perimeters 2 and if and only if it has the form T(A) = UAV or T(A) = with some invertible matrices U and V.

Keywords

rank;perimeter;linear operator;(U, V)-operator;

Language

English

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