A simple proof of the classification of normal Toeplitz matrices
Akio Arimoto · Electronic Journal of Linear Algebra · 2002
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.