Linear operators preserving maximal column ranks of nonbinary boolean matrices

Seok-Zun Song; Sung-Dae Yang; Sung-Min Hong; Young-Bae Jun; Seon-Jeong Kim

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 2, page 255-265
  • ISSN: 1509-9415

Abstract

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The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.

How to cite

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Seok-Zun Song, et al. "Linear operators preserving maximal column ranks of nonbinary boolean matrices." Discussiones Mathematicae - General Algebra and Applications 20.2 (2000): 255-265. <http://eudml.org/doc/287735>.

@article{Seok2000,
abstract = {The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.},
author = {Seok-Zun Song, Sung-Dae Yang, Sung-Min Hong, Young-Bae Jun, Seon-Jeong Kim},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Boolean matrix; semiring; linear operator on matrices; congruence operator on matrices; maximal column rank of a matrix; Boolean rank of a matrix; Boolean matrices; semirings; linear operators on matrices; congruence operators on matrices; maximal column ranks of matrices; Boolean ranks of matrices},
language = {eng},
number = {2},
pages = {255-265},
title = {Linear operators preserving maximal column ranks of nonbinary boolean matrices},
url = {http://eudml.org/doc/287735},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Seok-Zun Song
AU - Sung-Dae Yang
AU - Sung-Min Hong
AU - Young-Bae Jun
AU - Seon-Jeong Kim
TI - Linear operators preserving maximal column ranks of nonbinary boolean matrices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 2
SP - 255
EP - 265
AB - The maximal column rank of an m by n matrix is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over a nonbinary Boolean algebra. We also characterize the linear operators which preserve the maximal column ranks of matrices over nonbinary Boolean algebra.
LA - eng
KW - Boolean matrix; semiring; linear operator on matrices; congruence operator on matrices; maximal column rank of a matrix; Boolean rank of a matrix; Boolean matrices; semirings; linear operators on matrices; congruence operators on matrices; maximal column ranks of matrices; Boolean ranks of matrices
UR - http://eudml.org/doc/287735
ER -

References

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  1. [1] L.B. Beasley and N.J. Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77. Zbl0536.20044
  2. [2] L.B. Beasley and N.J. Pullman, Semiring rank versus column rank, Linear Algebra Appl. 101 (1988), 33-48. Zbl0642.15002
  3. [3] S.G. Hwang, S.J. Kim and S.Z. Song, Linear operators that preserve maximal column rank of Boolean matrices, Linear and Multilinear Algebra 36 (1994), 305-313. Zbl0804.15002
  4. [4] S. Kirkland and N. J. Pullman, Linear operators preserving invariants of nonbinary matrices, Linear and Multilinear Algebra 33 (1992), 295-300. Zbl0847.15006
  5. [5] S.Z. Song, Linear operators that preserve Boolean column ranks, Proc. Amer. Math. Soc. 119 (1993), 1085-1088. Zbl0802.15006
  6. [6] J.H.M. Wedderburn, Boolean linear associative algebra, Ann. of Math. 35 (1934), 185-194. Zbl0009.10002

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