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Linear Operators which Preserve Pairs on which the Rank is Additive
Beasley, LeRoy B. 한국산업정보응용수학회 1998 한국산업정보응용수학회 Vol.2 No.2
Let A and B be m x n matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A+B) = rank(A) +rank(B) implies that rank(T(A) + T(B)) = rankT(A) + rankT(B). We characterize the set of all linear operators which preserve the set of pairs of n x n matrices on which the rank is additive.
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.
A comparison of term ranks of symmetric matrices and their preservers
Beasley, L.B.,Song, S.Z.,Kang, K.T.,Lee, S.G. North Holland [etc.] 2013 Linear algebra and its applications Vol.438 No.10
This paper concerns three notions of matrix functions over semirings; term rank, reduced term rank and star cover number. We compare these matrix functions and we study those linear operators that preserve these matrix functions of nxn symmetric matrices with zero diagonal. In particular, we obtain important characterizations of term-rank (reduced term rank, star cover number) preservers with respect to a term rank (a reduced term rank, a star cover number, respectively) and a special matrix.
Linear operators that preserve zero-term rank over fields and rings
Beasley, Leroy B.,Song, Seok-Zun 濟州大學校 基礎科學硏究所 2002 基礎科學硏究 Vol.15 No.2
The zero-term rank of a matrix is the maximum number of zeros in any generalized diagonal. This article characterrizes the linear operators that preserve zero-term rank of m × n matrices when the matrices have entries either in a field with at least mn +2 elements or in a ring whose characteristic is not 2.
Linear preservers of zeros of matrix polynomials
Beasley, LeRoy B.,Guterman, Alexander E.,Lee, Sang-Gu,Song, Seok-Zun Elsevier 2005 Linear algebra and its applications Vol.401 No.-
<P><B>Abstract</B></P><P>We classify linear operators on matrices with semiring entries that preserve the zeros of multivariable matrix polynomials. These matrix polynomials are defined via the adjoint operator ([<I>X</I>,<I>Y</I>]=<I>XY</I>−<I>YX</I>) as if the matrices were being considered as if over a field. Also we compare the results over fields with the results over semirings.</P>
Triangular Normed Fuzzification of (Implicative) Filters in Lattice Implication Algebras
Beasley, Leroy B.,Cheon, Gi-Sang,Jun, Young-Bae,Song, Seok-Zun Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.2
We obtain characterizations of T-fuzzy (implicative) filters and some properties of T-product of fuzzy (implicative) filters in lattice implication algebras. We also establish the extension property for T-fuzzy implicative filters.
RANK INEQUALITIES OVER SEMIRINGS
BEASLEY LeRoy B.,GUTERMAN ALEXANDER E. Korean Mathematical Society 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.
RESOLUTION OF THE CONJECTURE ON STRONG PRESERVERS OF MULTIVARIATE MAJORIZATION
Beasley, Leroy-B.,Lee, Sang-Gu,Lee, You-Ho Korean Mathematical Society 2002 대한수학회보 Vol.39 No.2
In this paper, we will investigate the set of linear operators on real square matrices that strongly preserve multivariate majorisation without any additional conditions on the operator. This answers earlier conjecture on nonnegative matrices in [3] .
Preservers of term ranks of symmetric matrices
Beasley, L.B.,Song, S.Z.,Kang, K.T. North Holland [etc.] 2012 Linear algebra and its applications Vol.436 No.6
The term rank of an nxn matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we study linear operators that preserve term ranks of nxn symmetric matrices with entries in a commutative antinegative semiring & and with all diagonal entries zero. Consequently, we show that a linear operator T on symmetric matrices with zero diagonal preserves term rank if and only if T preserves term ranks 2 and k(>=3) if and only if T preserves term ranks 3 and k(>=4). Other characterizations of term-rank preservers are also given.
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.