A Simple Proof of the Classification of Normal Toeplitz Matrices

Details A Simple Proof of the Classification of Normal Toeplitz Matrices A Simple Proof of the Classification of Normal Toeplitz Matrices

2002-04-23

arxiv.org/abs/math/0204276v1

Mathematics

Rings and Algebras

5 pages

Scientific paper

We give an easy proof to show that every complex normal Toeplitz matrix is classified as either of type I or of type II. 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, we show that a real normal Toeplitz matrix must be one of four types: symmetric, skew-symmetric, circulant, or skew-circulant. Here we use trigonometric polynomials in the complex case and algebraic polynomials in the real case.

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