On spectral properties of group circulant matrices (Q2850043)

The author studies group circulant matrices induced by the convolution operator on \(\ell ^2(G)\) by a function \(\psi \in \ell ^2(G)\), where \(G\) is a finite group (typically non-abelian) and \(\ell ^2(G)\) is a finite-dimensional Hilbert space of all complex-valued functions for which elements of \(G\) form the orthonormal basis. In the non-abelian case, group circulant matrices are typically non-normal and possibly non-diagonalizable. The author obtains results on geometric properties of their eigenspace decompositions and diagonalizations (or Jordan decompositions). He obtains results for dihedral circulant matrices where the underlying group is the dihedral group \(D_n\) with \(n\) even.