LINEAR OPERATORS THAT PRESERVE PERIMETERS OF MATRICES OVER SEMIRINGS

Title & Authors
LINEAR OPERATORS THAT PRESERVE PERIMETERS OF MATRICES OVER SEMIRINGS
Song, Seok-Zun; Kang, Kyung-Tae; Beasley, Leroy B.;

Abstract
A rank one matrix can be factored as $\small{\mathbf{u}^t\mathbf{v}}$ for vectors $\small{\mathbf{u}}$ and $\small{\mathbf{v}}$ of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in $\small{\mathbf{u}}$ plus the number of nonzero entries in $\small{\mathbf{v}}$. A matrix of rank k is the sum of k rank one matrices. The perimeter of a matrix of rank k is the minimum of the sums of perimeters of the rank one matrices. In this article we characterize the linear operators that preserve perimeters of matrices over semirings.
Keywords
linear operator;perimeter;(U,V)-operator;
Language
English
Cited by
1.
Symmetric arctic ranks of nonnegative matrices and their linear preservers, Linear and Multilinear Algebra, 2017, 1
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