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Resolution of the conjecture on strong preservers of multivariate majorization
LeRoy B. Beasley,이상구,이유호 대한수학회 2002 대한수학회보 Vol.39 No.2
In this paper, we will investigate the set of linear operatorson real square matrices that strongly preserve multivariatemajorization without any additional conditions on the operator.This answers earlier conjecture on nonnegative matrices in cite{BLL}.
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.
Isolation numbers of integer matrices and their preservers
LeRoy B. Beasley,강경태,송석준 대한수학회 2020 대한수학회보 Vol.57 No.3
Let $A$ be an $m\times n$ matrix over nonnegative integers. The isolation number of $A$ is the maximum number of isolated entries in $A$. We investigate linear operators that preserve the isolation number of matrices over nonnegative integers. We obtain that $T$ is a linear operator that strongly preserve isolation number $k$ for $1\le k\le \min\{m,n\}$ if and only if $T$ is a ($P,Q$)-operator, that is, for fixed permutation matrices $P$ and $Q$, $T(A) = PAQ$ or, $m=n$ and $T(A) = PA^t Q$ for any $m\times n$ matrix $A$, where $A^t $ is the transpose of $A$.