Normal Toeplitz Matrices

Abstract

It is well known from the work of Brown and Halmos [J. Reine Angew. Math., 213 (1963/1964), pp. 89–102] that an infinite Toeplitz matrix is normal if and only if it is a rotation and translation of a Hermitian Toeplitz matrix. In the present article we prove that all finite normal Toeplitz matrices are either generalised circulants or are obtained from Hermitian Toeplitz matrices by rotation and translation.