Linear operators that preserve Boolean rank of Boolean matrices

LeRoy B. Beasley; Seok-Zun Song

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 $2 \times 2$ 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 $m \times n$ 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 $n \times n$ 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 $n \times n$ all ones matrix. For an $m \times n$ Boolean matrix $M$ , its Boolean rank $b (M)$ is the smallest positive integer $b$ such that $M = A B$ for some $m \times b$ Boolean matrix $A$ and $b \times n$ Boolean matrix $B$ . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an $n \times n$ primitive matrix $M$ in terms of its Boolean rank $b (M)$ , and they also characterized...

Some Fixed Point Theorems in Boolean Algebra

Koriolan Gilezan (1980)

Publications de l'Institut Mathématique

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Triangular solutions of Boolean equations.

Banković, Dragić (1998)

Novi Sad Journal of Mathematics

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On proper subuniverses of a boolean algebra

Wroński, Stanisław (2015-10-26T10:14:52Z)

Acta Universitatis Lodziensis. Folia Mathematica

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Notes on unique solutions of boolean equations

D. Banković (1987)

Matematički Vesnik

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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].