Displaying similar documents to “Linear operators that preserve Boolean rank of Boolean matrices”

Linear operators that preserve graphical properties of matrices: isolation numbers

LeRoy B. Beasley, Seok-Zun Song, Young Bae Jun (2014)

Czechoslovak Mathematical Journal

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Let A be a Boolean { 0 , 1 } matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A . A linear operator on the set of m × n Boolean matrices is a mapping which is additive and maps the zero matrix, O , to itself. A mapping strongly preserves a set, S , if it maps the set S into the set S and the complement...

The primitive Boolean matrices with the second largest scrambling index by Boolean rank

Yan Ling Shao, Yubin Gao (2014)

Czechoslovak Mathematical Journal

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The scrambling index of an n × n primitive Boolean matrix A is the smallest positive integer k such that A k ( A T ) k = J , where A T denotes the transpose of A and J denotes the n × n all ones matrix. For an m × n Boolean matrix M , its Boolean rank b ( M ) is the smallest positive integer b such that M = A B for some m × b Boolean matrix A and b × n Boolean matrix B . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an n × n primitive matrix M in terms of its Boolean rank b ( M ) , and they also characterized...

On Boolean modus ponens.

Sergiu Rudeanu (1998)

Mathware and Soft Computing

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An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].

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 (2000)

Discussiones Mathematicae - General Algebra and Applications

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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.