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.