Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2013.53.2.273
Title & Authors
Sets of Integer Matrix Pairs Derived from Row Rank Inequalities and Their Preservers Song, Seok-Zun; Jun, Young-Bae;
In this paper, we consider the row rank inequalities derived from comparisons of the row ranks of the additions and multiplications of nonnegative integer matrices and construct the sets of nonnegative integer matrix pairs which is occurred at the extreme cases for the row rank inequalities. We characterize the linear operators that preserve these extreme sets of nonnegative integer matrix pairs.
semiring;linear operator;row rank;(P,Q)-operator;
L. B. Beasley, A. E. Guterman, Rank inequalities over semirings, Journal of the Korean Math. Soc., 42(2)(2005), 223-241.
L. B. Beasley, A. E. Guterman, Linear preservers of extremes of rank inequalities over semirings, Factor rank, Journal of Mathematical Sciences (New York), 131(2005), 5919-5938.
L. B. Beasley, A. E. Guterman, C. L. Neal, Linear preservers for Sylvester and Frobe-nius bounds on matrix rank, Rocky Mountains J. of Mathematics, 36(1)(2006), 67-80.
L. B. Beasley, S.-G. Lee, S.-Z. Song, Linear operators that preserve pairs of matrices which satisfy extreme rank properties, Linear Algebra Appl., 350(2002), 263-272.
L. B. Beasley, S. Z. Song, K. T. Kang and B. K. Sarma, Column ranks and their preservers over nonnegative real matrices, Linear Algebra Appl. 399(2005), 3-16.
P. Pierce and others, A Survey of Linear Preserver Problems, Linear and Multilinear Algebra, 33(1992), 1-119.