Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

FACTOR RANK COMPARISONS OF MATRICES OVER TWO RELATED SEMIRINGS

  • Song Seok-Zun (Department of Mathematics Cheju National University)
  • Published : 2006.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

We consider matrices whose entries can be viewed as elements of both nonnegative integers and nonnegative rational numbers. We determine the differences of factor rank of matrices over the two semirings.

Keywords

References

  1. L. B. Beasley, D. A. Gregory and N. J. Pullman, Nonnegative rank-preserving operators, Linear Algebra Appl. 65 (1985), 207-223 https://doi.org/10.1016/0024-3795(85)90098-9
  2. L. B. Beasley, S. J. Kirkland and B. L. Shader, Rank comparisons, Linear Algebra Appl. 221 (1995), 171-188 https://doi.org/10.1016/0024-3795(93)00242-R
  3. L. B. Beasley and N. J. Pullman, Semiring rank versus column rank, Linear Algebra Appl. 101 (1988), 33-48 https://doi.org/10.1016/0024-3795(88)90141-3
  4. L. B. Beasley and S. Z. Song, A comparison of nonnegative real ranks and their preservers, Linear and Multilinear Algebra 31 (1992), 37-46 https://doi.org/10.1080/03081089208818120
  5. L. B. Beasley, S. Z. Song, K. T. Kang and B. K. Sarma, Column ranks and their preservers over nonnegative real, Linear Algebra Appl. 399 (2005), 3-16 https://doi.org/10.1016/S0024-3795(01)00431-1
  6. S. Z. Song, A comparison of maximal column ranks of matrices over related semirings, J. Korean Math. Soc. 34 (1997), no. 1, 51-61
  7. S. Z. Song, Linear operators that preserve maximal column ranks of nonnegative integer matrices ,Proc. Amer. Math. Soc. 124(4) (1998), 2205-2211
  8. S. Z. Song, K. T. Kang and Y. B. Jun, Rank-preserving operators of nonnegative integer matrices, Commun. Korean Math. Soc. 20 (2005), no. 4, 671-683 https://doi.org/10.4134/CKMS.2005.20.4.671