Off-Diagonal Elements of Normal Matrices.

摘要

Let A be an nxn complex matrix, and let W(A) denote the numerical range of A. In this paper, results of Parker and Mirsky are shown to be a consequence of the following fact. If A is normal, then the maximum value of (Ax,y) as x and y run over all ortho-normal pairs in C to the nth power coincides with the radius of the smallest closed disk in C which contains W(A). (Author)