Linear transformations that preserve term rank between different matrix spaces
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The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks k and l.
Abstract
The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks k and l.
참고문헌 (5)
- L. B. Beasley, "Preserving regular tournaments and term rank-1", Linear Algebra Appl, 431(5-7), pp.926~936 (2009)
- L. B. Beasley, "Term-rank, permanent, and rook-polynomial preservers", Linear Algebra Appl, 90, pp.33~46 (1987)
- L. B. Beasley, "Linear operators that preserve term rank 1", Proc. Roy. Irish Acad. Sect. A, 91(1), pp.71~78 (1991)
- R. Brualdi, "Combinatorial Matrix Theory" (1991), Cambridge University Press
- K. T. Kang, "Linear preservers of term ranks of matrices over semirings", Linear Algebra Appl, 436(7), pp.1850~1862 (2012)