Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES

  • Received : 2012.01.14
  • Published : 2013.01.01
Download PDF
⟨ Previous Next ⟩

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 $l$.

Keywords

References

  1. L. B. Beasley, D. Brown, and A. E. Guterman, Preserving regular tournaments and term rank-1, Linear Algebra Appl. 431 (2009), no. 5-7, 926-936. https://doi.org/10.1016/j.laa.2009.03.046
  2. L. B. Beasley and N. J. Pullman, Term-rank, permanent, and rook-polynomial preservers, Linear Algebra Appl. 90 (1987), 33-46. https://doi.org/10.1016/0024-3795(87)90302-8
  3. L. B. Beasley and N. J. Pullman, Linear operators that preserve term rank 1, Proc. Roy. Irish Acad. Sect. A 91 (1991), no. 1, 71-78.
  4. R. Brualdi and H. Ryser, Combinatorial Matrix Theory, Cambridge University Press, New York, 1991.
  5. K. T. Kang, S. Z. Song, and L. B. Beasley, Linear preservers of term ranks of matrices over semirings, Linear Algebra Appl. 436 (2012), no. 7, 1850-1862. https://doi.org/10.1016/j.laa.2011.08.046

Cited by

  1. LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES vol.52, pp.3, 2015, https://doi.org/10.4134/JKMS.2015.52.3.625
  2. CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES vol.21, pp.2, 2014, https://doi.org/10.7468/jksmeb.2014.21.2.121