2002/04/23 by Akio Arimoto, Arimoto, Akio
Mathematics · #15A57 #47B15 #47B35 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:15A57 #msc:47B15 #msc:47B35
paper · pdf · doi:10.48550/arxiv.math/0204276
5 pages
arxiv created 2002/04/23 · arxiv updated 2009/11/30
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.