Eigenvectors of Compound-Circulant and Alternating Circulant Matrices

Abstract

A circulant matrix whose elements are square submatrices is called a compound-circulant matrix. The eigenvectors and eigenvalues had been found for symmetric compound-circulant matrices, and that method is extended to general compound-circulant matrices. That analysis is applied to Stephen J. Watson's alternating circulant matrices, which reduce to compound-circulant matrices with square submatrices of order 2.