On EP matrices, partial isometry matrices and their numerical range

Abstract

In this paper, some properties of the numerical range of some well-known generalized inverses of matrices, such as Moore-Penrose inverse, Drazin inverse, DMP inverse and CMP inverse, are investigated. In particular, an identification of EP matrices is given via the numerical range. Also, some relations between certain orders and numerical ranges of matrices that are ordered, are presented. Moreover, some results related to the sharp points of the numerical range of a partial isometry matrix are obtained. To illustrate the main results, some numerical examples are also given.