2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63889We 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.5 pagesRings and Algebras15A57;47B15;47B35text