Left and right power-EP matrices
Cang Wu, Jianlong Chen · Linear and Multilinear Algebra · 2022
A square complex matrix A is EP if it satisfies R(A)=R(A∗) (or, equivalently, R(A)⊆R(A∗)). This paper aims to introduce two natural generalizations of EP matrices: a square matrix A is defined to be left or right power-EP if it satisfies R(Am)⊆R(A∗) or N(A∗)⊆N(Am) for some integer m≥ 0, respectively. Some properties, characterizations and applications of these two classes of matrices are given.