ELA, Volume 9, pp. 108-111, June 2002, abstract.
A Simple Proof of the Classification of Normal
Toeplitz Matrices
Akio Arimoto
An easy proof to show that every complex normal
Toeplitz matrix is classified as either of type I
or of type II is given. Instead of difference
equations on elements in the matrix used in past
studies, polynomial equations with coefficients
of elements are used. In a similar fashion, it is
shown that a real normal Toeplitz matrix must be
one of four types: symmetric, skew-symmetric,
circulant, or skew-circulant. Here trigonometric
polynomials in the complex case and algebraic
polynomials in the real case are used.