On sectorial matrices

A square complex matrix A is said to be sectorial if the values of the corresponding quadratic form x*Ax belong to the sector {z : \ arg z\ less than or equal to alpha} of the complex plane with a alpha is an element of [0, pi/2). We prove criterions for square matrix to be sectorial. The case of sectorial block matrix is considered and the corresponding criterions by means of Schur complements and quadratic forms are established. We also consider square matrices of the class 1 connected with sectorial matrices via the Cayley transform. (C) 2003 Elsevier Inc. All rights reserved.