Some new characterizations of bi-dagger matrices

Abstract

The concept of the bi-dagger matrix was introduced by Hartwig and Spindelböck [7]. In this paper, we provide some new characterizations of bi-dagger matrices. We prove that the index of a bi-dagger matrix is less than or equal to 2 and that a matrix is bi-dagger if and only if it is i-EP, and its index is less than or equal to 2. Specifically, a matrix is bi-dagger if and only if it commutes with its B-T inverse. Finally, we consider Problem 5 in [7] and establish conditions under which a bi-dagger matrix implies bi-normality.