DOI QR코드

DOI QR Code

RANK PRESERVER OF BOOLEAN MATRICES

  • Published : 2005.08.01

Abstract

A Boolean matrix with rank 1 is factored as a left factor and a right factor. The perimeter of a rank-1 Boolean matrix is defined as the number of nonzero entries in the left factor and the right factor of the given matrix. We obtain new characterizations of rank preservers, in terms of perimeter, of Boolean matrices.

Keywords

perimeter;linear operator;(U, V)-operator

References

  1. 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
  2. D. de Caen and D. A. Gregory, Primes in the semigroup of Boolean matrices, Linear Algebra Appl. 37 (1981), 119-134 https://doi.org/10.1016/0024-3795(81)90172-5
  3. S. G. Hwang, S. J. Kim, and S. Z. Song, Linear operators that preserve maximal column rank of Boolean matrices, Linear Multilinear Algebra 36 (1994), 305-313 https://doi.org/10.1080/03081089408818305
  4. S. Z. Song, L. B. Beasley, G. S. Cheon, and J. B. Jun, Rank and perimeter preservers of Boolean rank-1 matrices, J. Korean Math. Soc. 41 (2004), 397- 406 https://doi.org/10.4134/JKMS.2004.41.2.397
  5. S. Z. Song, Linear operators that preserve column rank of Boolean matrices, Proc. Amer. Math. Soc. 119 (1993), 1085-1088
  6. 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