대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제46권2호
  • /
  • Pages.373-385
  • /
  • 2009
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

BOOLEAN REGULAR MATRICES AND THEIR STRONGLY PRESERVERS

  • 발행 : 2009.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

An m${\times}$n Boolean matrix A is called regular if there exists an n${\times}$m Boolean matrix X such that AXA = A. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.

키워드

참고문헌

  1. L. B. Beasley and N. J. Pullman, Boolean-rank-preserving operators and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984), 55–77 https://doi.org/10.1016/0024-3795(84)90158-7
  2. J. Denes, Transformations and transformation semigroups, Seminar Report, University of Wisconsin, Madison, Wisconsin, 1976
  3. K. H. Kim, Boolean Matrix Theory and Applications, Pure and Applied Mathematics, Vol. 70, Marcel Dekker, New York, 1982
  4. R. D. Luce, A note on Boolean matrix theory, Proc. Amer. Math. Soc. 3 (1952), 382–388 https://doi.org/10.2307/2031888
  5. E. H. Moore, General analysis, Part I, Mem. of Amer. Phil. Soc. 1 (1935)
  6. R. J. Plemmons, Generalized inverses of Boolean relation matrices, SIAM J. Appl. Math. 20 (1971), 426–433 https://doi.org/10.1137/0120046
  7. P. S. S. N. V. Prasada Rao and K. P. S. Bhaskara Rao, On generalized inverses of Boolean matrices, Linear Algebra and Appl. 11 (1975), no. 2, 135–153
  8. D. E. Rutherford, Inverses of Boolean matrices, Proc. Glasgow Math. Assoc. 6 (1963), 49–53
  9. S. Z. Song, Linear operators that preserve column rank of Boolean matrices, Proc. Amer. Math. Soc. 119 (1993), no. 4, 1085–1088
  10. S. Z. Song and K. T. Kang, Linear maps that preserve commuting pairs of matrices over general Boolean algebra, J. Korean Math. Soc. 43 (2006), no. 1, 77–86 https://doi.org/10.4134/JKMS.2006.43.1.077

피인용 문헌

  1. On linear operators strongly preserving invariants of Boolean matrices vol.62, pp.1, 2012, https://doi.org/10.1007/s10587-012-0004-y