Some (Hopf) algebraic properties of circulant matrices

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.