Displaying similar documents to “Linear preservers of regular matrices over general Boolean algebras.”

Linear maps that strongly preserve regular matrices over the Boolean algebra

Kyung-Tae Kang, Seok-Zun Song (2011)

Czechoslovak Mathematical Journal

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The set of all m × n Boolean matrices is denoted by 𝕄 m , n . We call a matrix A ∈ 𝕄 m , n regular if there is a matrix G ∈ 𝕄 n , m such that A G A = A . In this paper, we study the problem of characterizing linear operators on 𝕄 m , n that strongly preserve regular matrices. Consequently, we obtain that if min { m , n } ≤ 2 , then all operators on 𝕄 m , n strongly preserve regular matrices, and if min { m , n } ≥ 3 , then an operator T on 𝕄 m , n strongly preserves regular matrices if and only if there are invertible matrices U and V such that T ( X ) = U X V for all X ∈ 𝕄 m , n , or m = n and T ( X ) = U X T V for all...

On a construction of regular Hadamard matrices

David Benjamin Meisner (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We give a construction for regular Hadamard matrices of order a 2 ⁢ v where a ≠ 1 is the order of a Hadamard matrix and v is the order of a regular Hadamard matrix. The construction can be used to construct regular Hadamard matrices with special properties and includes several constructions which have been given previously. In the final section we consider the case a = 2 in more detail.

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...

Combinatorial aspects of generalized complementary basic matrices

Miroslav Fiedler, Frank Hall (2013)

Open Mathematics

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This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.