Linear operators preserving maximal column ranks of nonbinary boolean matrices

• Autorzy: Seok-Zun Song , Sung-Dae Yang , Sung-Min Hong , Young-Bae Jun , Seon-Jeong Kim
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Boolean matrix; semiring; linear operator on matrices; congruence operator on matrices; maximal column rank of a matrix; Boolean rank of a matrix

Kategorie tematyczne

• 06E05: Structure theory
• 16Y60: Semirings
• 15A04: Linear transformations, semilinear transformations
• 15A03: Vector spaces, linear dependence, rank

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 255-265

Daty

wydano

2000

otrzymano

1999-12-21

poprawiono

2000-06-20

Twórcy

autor

Seok-Zun Song

• Department of Mathematics, Cheju National University, Cheju, 690-756, South-Korea

autor

Sung-Dae Yang

• Department of Mathematics, Cheju National University, Cheju, 690-756, South-Korea

autor

Sung-Min Hong

• Department of Mathematics, Gyeongsang National University, Chinju, 660-701, South-Korea

autor

Young-Bae Jun

• Department of Mathematics, Gyeongsang National University, Chinju, 660-701, South-Korea

autor

Seon-Jeong Kim

• Department of Mathematics, Gyeongsang National University, Chinju, 660-701, South-Korea

Bibliografia

• [1] L.B. Beasley and N.J. Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77.
• [2] L.B. Beasley and N.J. Pullman, Semiring rank versus column rank, Linear Algebra Appl. 101 (1988), 33-48.
• [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.
• [4] S. Kirkland and N. J. Pullman, Linear operators preserving invariants of nonbinary matrices, Linear and Multilinear Algebra 33 (1992), 295-300.
• [5] S.Z. Song, Linear operators that preserve Boolean column ranks, Proc. Amer. Math. Soc. 119 (1993), 1085-1088.
• [6] J.H.M. Wedderburn, Boolean linear associative algebra, Ann. of Math. 35 (1934), 185-194.

Identyfikatory

DOI

10.7151/dmgaa.1021