Higher rank numerical hulls of matrices

Abstract

This is an exposition of some of the aspects of polynomial numerical hulls and higer rank numerical ranges of matrices. For any n × n matrix A, we use the joint higher rank numerical range, Λk(A, . . . , Am), to define the higher rank numerical hull of A. We characterize the higher rank numerical hulls of Hermitian matrices. Also, the higher rank numerical hulls of unitary matrices are studied.