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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.

On the combinatorial structure of 0 / 1 -matrices representing nonobtuse simplices

Jan Brandts, Abdullah Cihangir (2019)

Applications of Mathematics

A 0 / 1 -simplex is the convex hull of n + 1 affinely independent vertices of the unit n -cube I n . It is nonobtuse if none of its dihedral angles is obtuse, and acute if additionally none of them is right. Acute 0 / 1 -simplices in I n can be represented by 0 / 1 -matrices P of size n × n whose Gramians G = P P have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. In this paper, we will prove that the positive part D of the transposed inverse P - of P is doubly stochastic and has the same support...

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