DOI QR코드

DOI QR Code

LINEAR PRESERVERS OF BOOLEAN NILPOTENT MATRICES

  • Song, Seok-Zun (Department of Mathematics Cheju National University) ;
  • Kang, Kyung-Tae (Department of Mathematics Cheju National University) ;
  • Jun, Young-Bae (Department of Mathematics Education Gyeongsang National University)
  • 발행 : 2006.05.01

초록

For an $n{\times}n$ Boolean matrix A, A is called nilpotent if $A^m=O$ for some positive integer m. We consider the set of $n{\times}n$ nilpotent Boolean matrices and we characterize linear operators that strongly preserve nilpotent matrices over Boolean algebras.

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. L. B. Beasley and N. J. Pullman, Operators that preserve semiring matrix functions, Linear Algebra Appl. 99 (1988), 199-216 https://doi.org/10.1016/0024-3795(88)90132-2
  3. P. Botta, S. Pierce, and W. Watkins, Linear transformations that preserve the nilpotent matrices, Pacific J. Math. 104 (1983), no. 1, 39-46 https://doi.org/10.2140/pjm.1983.104.39
  4. K. H. Kim, Boolean matrix theory and applications, Pure and Applied Mathemat ics, Vol. 70, Marcel Dekker, New York, 1982
  5. S. Kirkland and N. J. Pullman, Linear operators preserving invariants of non- binary matrices, Linear Multilinear Algebra 33 (1993), 295-300
  6. S. -Z. Song, L. B. Beasley, G. -S. Cheon, and Y. -B. Jun, Rank and perimeter preservers of Boolean rank-1 matrices, J. Korean Math. Soc. 41 (2004), no. 2, 397-406 https://doi.org/10.4134/JKMS.2004.41.2.397
  7. S. -Z. Song and S. -G. Lee, Column ranks and their preservers of general Boolean matrices, J. Korean Math. Soc. 32 (1995), no. 3, 531-540

피인용 문헌

  1. Regular matrices and their strong preservers over semirings vol.429, pp.1, 2008, https://doi.org/10.1016/j.laa.2008.02.015
  2. The Invertible Linear Operator Preserving {1,2}-Inverses of Matrices over Semirings vol.05, pp.01, 2015, https://doi.org/10.12677/PM.2015.51002
  3. Primitive symmetric matrices and their preservers vol.65, pp.1, 2017, https://doi.org/10.1080/03081087.2016.1175414
  4. Zero-term rank and zero-star cover number of symmetric matrices and their linear preservers vol.64, pp.12, 2016, https://doi.org/10.1080/03081087.2016.1155534
  5. On linear operators strongly preserving invariants of Boolean matrices vol.62, pp.1, 2012, https://doi.org/10.1007/s10587-012-0004-y