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Algebra and Discrete Mathematics, 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
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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.
Received: 03.12.2011
Accepted: 03.12.2011
Bibliographic databases:
Document Type: Article
MSC: 15B05; 16W30
Language: English
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{https://mathscinet.ams.org/mathscinet-getitem?mr=2963821}
\zmath{https://zbmath.org/?q=an:06120558}
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