On the Further Properties of the MPBT Inverse and Applications to Special Matrices

This paper aims to simplify the form of the MPBT inverse, further explore its properties, and discuss when it coincides with other generalized inverses. Notably, the MPBT inverse coincides with the Moore–Penrose inverse when the index of the matrix is at most 1; the MPBT inverse equals the MPCEP-inverse when the index of the matrix is at most 2. Additionally, new characterizations of bi-EP matrices are presented, based on some properties of the MPBT inverse. Finally, MPBT matrices constructed via the MPBT inverse are shown to be equal to B-T matrices.