LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES

Title & Authors
LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES
Song, Seok-Zun; Beasley, Leroy B.;

Abstract
The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks $\small{k}$ and $\small{l}$.
Keywords
semiring;term rank;linear transformation;
Language
English
Cited by
1.
CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES,;;;

한국수학교육학회지시리즈B:순수및응용수학, 2014. vol.21. 2, pp.121-128
2.
LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES,;;;

대한수학회지, 2015. vol.52. 3, pp.625-636
1.
LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES, Journal of the Korean Mathematical Society, 2015, 52, 3, 625
2.
CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES, The Pure and Applied Mathematics, 2014, 21, 2, 121
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