It is well-known from the work of A. Brown and P.R. Halmos that an infinite Toeplitz matrix is normal if and only if it is a rotation and translation of a Hermitian Toeplitz matrix. In the present article we prove that all finite normal Toeplitz matrices are either generalised circulants or are obtained from Hermitian Toeplitz matrices by rotation and translation. ∗Supported in part by an NSERC...

A list of seventy conditions on an n {by{ n complex matrix A , equivalent to its being normal, published nearly ten years ago by Grone, Johnson, Sa, and Wolkowicz has proved to be very useful. Hoping that, in an extended form, it will be even more helpful, we compile here another list of about twenty conditions. They either have been overlooked by the authors of the original list or have appear...

In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.