RANK-PRESERVING OPERATORS OF NONNEGATIVE INTEGER MATRICES

- Journal title : Communications of the Korean Mathematical Society
- Volume 20, Issue 4, 2005, pp.671-683
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2005.20.4.671

Title & Authors

RANK-PRESERVING OPERATORS OF NONNEGATIVE INTEGER MATRICES

SONG, SEOK-ZUN; KANG, KYUNG-TAE; JUN, YOUNG-BAE;

SONG, SEOK-ZUN; KANG, KYUNG-TAE; JUN, YOUNG-BAE;

Abstract

The set of all matrices with entries in is denoted by . We say that a linear operator T on is a (U, V)-operator if there exist invertible matrices and such that either T(X) = UXV for all X in , or m = n and T(X) = for all X in . In this paper we show that a linear operator T preserves the rank of matrices over the nonnegative integers if and only if T is a (U, V)operator. We also obtain other characterizations of the linear operator that preserves rank of matrices over the nonnegative integers.

Keywords

semidomain;(U, V)-operator;rank preserver;

Language

English

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