Rank-preserver of Matrices over Chain Semiring
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For a rank-1 matrixA, there is a factorization asA = abt, the product of twovectorsa and b. We characterize the linear operators that preserve rank and some equiv-alent condition of rank-1 matrices over a chain semiring. We also obtain a linear operatorT preserves the rank of rank-1 matrices if and only if it is a form (P;Q;B)-operator withappropriate permutation matrices P and Q, and a matrixB with all nonzero entries.
Abstract
For a rank-1 matrixA, there is a factorization asA = abt, the product of twovectorsa and b. We characterize the linear operators that preserve rank and some equiv-alent condition of rank-1 matrices over a chain semiring. We also obtain a linear operatorT preserves the rank of rank-1 matrices if and only if it is a form (P;Q;B)-operator withappropriate permutation matrices P and Q, and a matrixB with all nonzero entries.
참고문헌 (4)
- L. B. Beasley, "Boolean rank-preserving operators and Booleanrank-1 spaces", 59, pp.55~77 (1984)
- L. B. Beasley, "Fuzzy Rank-Preserving Operators", 73, pp.197~211 (1986)
- S. Z. Song, "Linear operators that preservecolumn rank of fuzzy matrices", 62, pp.311~317 (1994)
- S. Z. Song, "Rank and perimeter preservers of Boolean rank-$1$ matrices}", 41(2), pp.397~406 (2004)