[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180771

STRONG PRESERVERS OF SYMMETRIC ARCTIC RANK OF NONNEGATIVE REAL MATRICES

Beasley, LeRoy B. (Department of Mathematics and Statistics Utah State University)
Encinas, Luis Hernandez (Institute of Physical and Information Technologies Spanish National Research Council (CSIC))
Song, Seok-Zun (Department of Mathematics Jeju National University)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.6, 2019 , pp. 1503-1514 More about this Journal

Abstract

A rank 1 matrix has a factorization as $uv^t$ for vectors u and v of some orders. The arctic rank of a rank 1 matrix is the half number of nonzero entries in u and v. A matrix of rank k can be expressed as the sum of k rank 1 matrices, a rank 1 decomposition. The arctic rank of a matrix A of rank k is the minimum of the sums of arctic ranks of the rank 1 matrices over all rank 1 decomposition of A. In this paper we obtain characterizations of the linear operators that strongly preserve the symmetric arctic ranks of symmetric matrices over nonnegative reals.

Keywords

linear operator; ( $P,P^t,B$ )-operator; weighted cell; symmetric arctic rank;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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