Sets of Integer Matrix Pairs Derived from Row Rank Inequalities and Their Preservers
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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.
Abstract
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.
참고문헌 (6)
- LeRoy B. Beasley, "RANK INEQUALITIES OVER SEMIRINGS", 대한수학회지, 42(2), pp.33~51 (2005), 대한수학회
- L. B. Beasley, "Linear preservers of extremes of rank inequalities over semirings, Factor rank", Journal of Mathematical Sciences, 131, pp.5919~5938 (2005)
- L. B. Beasley, "Linear preservers for Sylvester and Frobe- nius bounds on matrix rank", Rocky Mountains J. of Mathematics, 36(1), pp.67~80 (2006)
- L. B. Beasley, "Linear operators that preserve pairs of matrices which satisfy extreme rank properties", Linear Algebra Appl, 350, pp.263~272 (2002)
- L. B. Beasley, "Column ranks and their preservers over nonnegative real matrices", Linear Algebra Appl, 399, pp.3~16 (2005)
- P. Pierce, "A Survey of Linear Preserver Problems", Linear and Multilinear Algebra, 33, pp.1~119 (1992)