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http://dx.doi.org/10.4134/JKMS.2013.50.1.127

LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES  

Song, Seok-Zun (Department of Mathematics Jeju National University)
Beasley, Leroy B. (Department of Mathematics Jeju National University)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 127-136 More about this Journal
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 $k$ and $l$.
Keywords
semiring; term rank; linear transformation;
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