Linear Operators that Preserve Term Ranks of Matrices over Semirings
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 3
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The term rank of a matrix $A$ is the least number of lines (rows or columns) needed to include all the nonzero entries in $A$, and is a well-known upper bound for many standard and non-standard matrix ranks, and is one of the most important combinatorially. In this paper, we obtain a characterization of linear operators that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear operator $T$ on a matrix space over antinegative semirings preserves term rank if and only if $T$ preserves any two term ranks $k$ and $l$ if and only if $T$ strongly preserves any one term rank $k$.
Classification :
15A86, 15A03, 15A04
@article{BMMS_2014_37_3_a9,
author = {Leroy B. Beasley and Seok-Zun Song},
title = {Linear {Operators} that {Preserve} {Term} {Ranks} of {Matrices} over {Semirings}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2014},
volume = {37},
number = {3},
url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_3_a9/}
}
Leroy B. Beasley; Seok-Zun Song. Linear Operators that Preserve Term Ranks of Matrices over Semirings. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2014_37_3_a9/