On the Eigenvectors of Generalized Circulant Matrices - Andrade, Enide (2024)
In \cite{Mourad}, Kaddoura and Mourad, in order to widen the scope of the class of circulant matrices, (see \cite{Davis}), constructed circulant-like matrices that were called generalized weighted circulant matrices. These matrices form a class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. The characteristic polynomials, eigenvalues and eigenvectors of the generalized permutation matrices corresponding to a family of permutations were described. Additionally, the eigenvalues of the weighted circulant matrices were given. However, their eigenvectors were not studied. Having these results as motivation, we present, in some cases, explicit formulas for the eigenvectors of the generalized weighted circulant matrices. In this work, they are simply called generalized circulant matrices.