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BEASLEY, LEROY B.,SONG, SEOK-ZUN,LEE, SANG-GU 제주대학교 기초과학연구소 2002 基礎科學硏究 Vol.15 No.1
We obtain characterizations of those linear operators that preserve zero-term rank on the m×n matrices over antinegative semirings. That is, a linear operator T preserves zero-term rank if and only if it has the form T(X) = P(B_(o)X)Q, where P, Q are permutation matrices and B_(o)X is the Schur product with B whose entries are all nonzero and not zero-divisors.
AN INEQUALITY ON PERMANENTS OF HADAMARD PRODUCTS
Beasley, Leroy B. Korean Mathematical Society 2000 대한수학회보 Vol.37 No.3
Let $A=(a_{ij}\ and\ B=(b_{ij}\ be\ n\times\ n$ complex matrices and let A$\bigcirc$B denote the Hadamard product of A and B, that is $AA\circB=(A_{ij{b_{ij})$.We conjecture a permanental analog of Oppenheim's inequality and verify it for n=2 and 3 as well as for some infinite classes of matrices.
Rank and perimeter preservers of boolean rank-1 matrices
송석준,LeRoy B. Beasley,Gi-Sang Cheon,Young-Bae Jun 대한수학회 2004 대한수학회지 Vol.41 No.2
For a Boolean rank-1 matrix A = abt, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the Boolean linear operators that preserve rank and perimeter of Boolean rank-1 matrices.
RANK AND PERIMETER PRESERVERS OF BOOLEAN RANK-1 MATRICES
Song, Seok-Zun,Beasley, Leroy-B.,Cheon, Gi-Sang,Jun, Young-Bae Korean Mathematical Society 2004 대한수학회지 Vol.41 No.2
For a Boolean rank-l matrix $A\;=\;ab^{t}$, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the Boolean linear operators that preserve rank and perimeter of Boolean rank-l matrices.
LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES
Leroy B. Beasley,강경태,송석준 대한수학회 2015 대한수학회지 Vol.52 No.3
The Boolean rank of a nonzero m × n Boolean matrix A is the least integer k such that there are an m× k Boolean matrix B and a k × n Boolean matrix C with A = BC. We investigate the structure of linear transformations T : M m,n → M p,q which preserve Boolean rank. We also show that if a linear transformation preserves the set of Boolean rank 1 matrices and the set of Boolean rank k matrices for any k, 2 ≤ k ≤ min{m, n} (or if T strongly preserves the set of Boolean rank 1 matrices), then T preserves all Boolean ranks.
RANK INEQUALITIES OVER SEMIRINGS
LeRoy B. Beasley,Alexander E. Guterman 대한수학회 2005 대한수학회지 Vol.42 No.2
Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings.
Linear Operators Strongly Preserving Multivariate Majorization with T(I) = I
LeRoy B. Beasley ...et al KYUNGPOOK UNIVERSITY 1999 Kyungpook mathematical journal Vol.39 No.1
In this paper, we will investigate the set of linear operators that strongly preserve multivariate majorization with some additional conditions. We determine the linear operators that strongly preserve multivariate majorization with T(I) = I and which map nonnegative matrices to nonnegative matrices.
EXTREME PRESERVERS OF TERM RANK INEQUALITIES OVER NONBINARY BOOLEAN SEMIRING
Beasley, LeRoy B.,Heo, Seong-Hee,Song, Seok-Zun Korean Mathematical Society 2014 대한수학회지 Vol.51 No.1
The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.