Displaying 101 – 120 of 138

Showing per page

Algorithm for the complement of orthogonal operations

Iryna V. Fryz (2018)

Commentationes Mathematicae Universitatis Carolinae

G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a k -tuple of orthogonal n -ary operations, where k < n , to an n -tuple of orthogonal n -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a k -tuple of orthogonal n -ary operations to an n -tuple of orthogonal n -ary operations and an algorithm for complementing a k -tuple of orthogonal k -ary operations to an n -tuple of orthogonal n -ary operations. Also we find some...

Analytic aspects of the circulant Hadamard conjecture

Teodor Banica, Ion Nechita, Jean-Marc Schlenker (2014)

Annales mathématiques Blaise Pascal

We investigate the problem of counting the real or complex Hadamard matrices which are circulant, by using analytic methods. Our main observation is the fact that for | q 0 | = ... = | q N - 1 | = 1 the quantity Φ = i + k = j + l q i q k q j q l satisfies Φ N 2 , with equality if and only if q = ( q i ) is the eigenvalue vector of a rescaled circulant complex Hadamard matrix. This suggests three analytic problems, namely: (1) the brute-force minimization of Φ , (2) the study of the critical points of Φ , and (3) the computation of the moments of Φ . We explore here these questions,...

Currently displaying 101 – 120 of 138