The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.