Linear maps that strongly preserve regular matrices over the Boolean algebra

Kyung-Tae Kang; Seok-Zun Song

Displaying similar documents to “Linear maps that strongly preserve regular matrices over the Boolean algebra”

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...

On linear operators strongly preserving invariants of Boolean matrices

Yizhi Chen, Xian Zhong Zhao (2012)

Czechoslovak Mathematical Journal

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Let $𝔹_{k}$ be the general Boolean algebra and $T$ a linear operator on $M_{m, n} (𝔹_{k})$ . If for any $A$ in $M_{m, n} (𝔹_{k})$ ( $M_{n} (𝔹_{k})$ , respectively), $A$ is regular (invertible, respectively) if and only if $T (A)$ is regular (invertible, respectively), then $T$ is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over $𝔹_{k}$ . Meanwhile, noting that a general Boolean algebra $𝔹_{k}$ is...

Linear preservers of regular matrices over general Boolean algebras.

Kang, Kyung-Tae, Song, Seok-Zun, Heo, Seong-Hee, Jun, Young-Bae (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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On block triangular matrices with signed Drazin inverse

Changjiang Bu, Wenzhe Wang, Jiang Zhou, Lizhu Sun (2014)

Czechoslovak Mathematical Journal

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The sign pattern of a real matrix $A$ , denoted by $sgn A$ , is the $(+, -, 0)$ -matrix obtained from $A$ by replacing each entry by its sign. Let $𝒬 (A)$ denote the set of all real matrices $B$ such that $sgn B = sgn A$ . For a square real matrix $A$ , the Drazin inverse of $A$ is the unique real matrix $X$ such that $A^{k + 1} X = A^{k}$ , $X A X = X$ and $A X = X A$ , where $k$ is the Drazin index of $A$ . We say that $A$ has signed Drazin inverse if $sgn {\tilde{A}}^{d} = sgn A^{d}$ for any $\tilde{A} \in 𝒬 (A)$ , where $A^{d}$ denotes the Drazin inverse of $A$ . In this paper, we give necessary conditions for some block triangular matrices...

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

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Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.