대한수학회지 (Journal of the Korean Mathematical Society)

  • 제50권1호
  • /
  • Pages.127-136
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  • 2013
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES

  • 투고 : 2012.01.14
  • 발행 : 2013.01.01
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초록

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 $l$.

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참고문헌

  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

피인용 문헌

  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