2014
DOI: 10.5666/kmj.2014.54.4.619
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Characterizations of Zero-Term Rank Preservers of Matrices over Semirings

Abstract: Abstract. Let M(S) denote the set of all m×n matrices over a semiring S. For A ∈ M(S), zero-term rank of A is the minimal number of lines (rows or columns) needed to cover all zero entries in A. In [5], the authors obtained that a linear operator on M(S) preserves zero-term rank if and only if it preserves zero-term ranks 0 and 1. In this paper, we obtain new characterizations of linear operators on M(S) that preserve zero-term rank. Consequently we obtain that a linear operator on M(S) preserves zero-term ran… Show more

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