Boolean-rank-preserving operators and Boolean-rank-1 spaces

Beasley, LeRoy B.; Pullman, Norman J.

doi:10.1016/0024-3795(84)90158-7

Cited by 61 publications

(35 citation statements)

References 12 publications

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“…If f is a function defined on M(S), then T preserves the function f if f (T (A)) = f (A) for all A ∈ M(S). There are many papers on linear operators that preserve matrix functions over S(see [1]- [6] and therein). Beasley and Pullman( [3]) characterized linear operators on M(S) that preserve term rank.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of Zero-Term Rank Preservers of Matrices over Semirings

Kang¹,

Shi²,

Beasley³

et al. 2014

Kyungpook mathematical journal

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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 rank if and only if it preserves two consecutive zero-term ranks k and k + 1, where 0 ≤ k ≤ min{m, n} − 1 if and only if it strongly preserves zero-term rank h, where 1 ≤ h ≤ min{m, n}.

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Section: Introductionmentioning

confidence: 99%

Characterizations of Zero-Term Rank Preservers of Matrices over Semirings

Kang¹,

Shi²,

Beasley³

et al. 2014

Kyungpook mathematical journal

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“…Several authors characterized those linear operators on M m,n (B) that (strongly) preserve various properties and functions defined on M m,n (B) ( [1], [9], [10]). …”

Section: Introductionmentioning

confidence: 99%

Boolean Regular Matrices and Their Strongly Preservers

Song¹,

Kang²,

Kang³

2009

Bulletin of the Korean Mathematical Society

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“…There are many papers on linear operators on a matrix space that preserve matrix functions over an algebraic structure ( [1], [2], [3] and [5]). Boolean matrices also have been the subject of research by many authors ( [2]- [5]).…”

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confidence: 99%

“…Boolean matrices also have been the subject of research by many authors ( [2]- [5]). Beasley and Pullman ( [2]) obtained characterizations of rank-preserving operators of Boolean matrices. Kang and Song ([3]) characterized the linear operators that preserve regular matrices over the Boolean algebra.…”

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confidence: 99%