JOURNAL BROWSE
Search
Advanced SearchSearch Tips
LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
LINEAR TRANSFORMATIONS THAT PRESERVE TERM RANK BETWEEN DIFFERENT MATRIX SPACES
Song, Seok-Zun; Beasley, Leroy B.;
  PDF(new window)
 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 and .
 Keywords
semiring;term rank;linear transformation;
 Language
English
 Cited by
1.
CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES,;;;

한국수학교육학회지시리즈B:순수및응용수학, 2014. vol.21. 2, pp.121-128 crossref(new window)
2.
LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES,;;;

대한수학회지, 2015. vol.52. 3, pp.625-636 crossref(new window)
1.
LINEAR PRESERVERS OF BOOLEAN RANK BETWEEN DIFFERENT MATRIX SPACES, Journal of the Korean Mathematical Society, 2015, 52, 3, 625  crossref(new windwow)
2.
CHARACTERIZATIONS OF BOOLEAN RANK PRESERVERS OVER BOOLEAN MATRICES, The Pure and Applied Mathematics, 2014, 21, 2, 121  crossref(new windwow)
 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. crossref(new window)

2.
L. B. Beasley and N. J. Pullman, Term-rank, permanent, and rook-polynomial preservers, Linear Algebra Appl. 90 (1987), 33-46. crossref(new window)

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. crossref(new window)