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.Comment: 5 page
