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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2012, Volume 13, Issue 1, Pages 1–17 (Mi adm61)

RESEARCH ARTICLE

Some (Hopf) algebraic properties of circulant matrices

Helen Albuquerquea, Florin Panaiteb

a Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal
b Institute of Mathematics of the Romanian Academy, PO-Box 1-764, RO-014700 Bucharest, Romania

Abstract: We study some (Hopf) algebraic properties of circulant matrices, inspired by the fact that the algebra of circulant $n\times n$ matrices is isomorphic to the group algebra of the cyclic group with $n$ elements. We introduce also a class of matrices that generalize both circulant and skew circulant matrices, and for which the eigenvalues and eigenvectors can be read directly from their entries.

Keywords: Hopf algebras; (generalized) circulant matrices; Brandt algebras.

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Bibliographic databases:
MSC: 15B05; 16W30
Accepted:03.12.2011
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Citation: Helen Albuquerque, Florin Panaite, “Some (Hopf) algebraic properties of circulant matrices”, Algebra Discrete Math., 13:1 (2012), 1–17

Citation in format AMSBIB
\Bibitem{AlbPan12} \by Helen~Albuquerque, Florin~Panaite \paper Some (Hopf) algebraic properties of circulant matrices \jour Algebra Discrete Math. \yr 2012 \vol 13 \issue 1 \pages 1--17 \mathnet{http://mi.mathnet.ru/adm61} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2963821} \zmath{https://zbmath.org/?q=an:06120558}