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Linear operators preserving maximal column ranks of nonbinary boolean matrices

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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.
Twórcy
  • Department of Mathematics, Cheju National University, Cheju, 690-756, South-Korea
  • Department of Mathematics, Cheju National University, Cheju, 690-756, South-Korea
  • Department of Mathematics, Gyeongsang National University, Chinju, 660-701, South-Korea
  • Department of Mathematics, Gyeongsang National University, Chinju, 660-701, South-Korea
  • 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.
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1021
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