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Linear preserver of n × 1 Ferrers vectors

Leila Fazlpar, Ali Armandnejad (2023)

Czechoslovak Mathematical Journal

Let A = [ a i j ] m × n be an m × n matrix of zeros and ones. The matrix A is said to be a Ferrers matrix if it has decreasing row sums and it is row and column dense with nonzero ( 1 , 1 ) -entry. We characterize all linear maps perserving the set of n × 1 Ferrers vectors over the binary Boolean semiring and over the Boolean ring 2 . Also, we have achieved the number of these linear maps in each case.

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

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.

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