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Title: Spectral properties of the binary Hadamard matrices
Authors: González, Luis 
Suárez Sarmiento, Antonio Félix 
UNESCO Clasification: 120110 Algebra lineal
Keywords: Hadamard matrix
Symmetric S-matrix
Skew-type S-matrix
Spectral properties, et al
Issue Date: 2020
Project: Integración de Nuevas Metodologías en Simulación de Campos de Viento, Radiación Solar y Calidad Del Aire 
Journal: Linear and Multilinear Algebra 
Abstract: A binary Hadamard matrix (also called an S-matrix) is an n x n (0,1) -matrix formed by taking an (n + 1 ) x (n + 1) Hadamard matrix in which the entries in the first row and column are +1, changing +1’s +1’s to 0's and -1’s to +1’s , and deleting the first row and column. In this paper, some spectral properties of the binary Hadamard matrices are derived. All singular values and eigenvalues' modulus of an arbitrary S-matrix are obtained. Two special types of binary Hadamard matrices, namely the symmetric and the skew-type ones, are analysed in more detail. In particular, we prove that an S-matrix Sn (regardless of its order n) is of skew type if, and only if, all its eigenvalues different from the largest one (in modulus) are imaginary and have real part 1/2. Finally, the symmetric and skew-symmetric parts of an S-matrix are analysed.
ISSN: 0308-1087
DOI: 10.1080/03081087.2018.1499705
Source: Linear & Multilinear Algebra [ISSN 0308-1087], v. 68 (1), p. 113-132, (Enero 2020)
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