Naslov
Morphisms of Butson classes

Autori
Egan, Ronan ; O Cathain, Padraig

Izvornik
Linear algebra and its applications (0024-3795) 577 (2019); 78-93

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Butson Hadamard matrix ; Morphism ; Eigenvalues

Sažetak
We introduce the concept of a morphism from the set of Butson Hadamard matrices over kth roots of unity to the set of Butson matrices over lth roots of unity. Tensor products give many examples of morphisms in which k divides l. More interesting are constructions where k does not divide l. Examples where this occurs include Turyn's construction of real Hadamard matrices from Butson matrices over the 4th roots and the work of Compton, Craigen and de Launey on ‘unreal’ Butson matrices over the 6th roots. We give a unified treatment of these constructions in terms of the eigenvalues and minimal polynomials of associated Butson matrices. We produce a new family of morphisms from sets of mutually unbiased bases constructed by Gow. We also classify all morphisms from the set of n x n Butson matrices over kth roots of unity to the set of 2n x 2n Butson matrices over th roots of unity where l<k.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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