Yuefeng Gao

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.

Let a ? R? ? R# in this paper. We give several characterizations for a to be an EP element or an Hermitian element in terms of reverse order laws of two elements from the given set.

The main purpose of this paper is to provide a solution of the consistent fuzzy linear system and a generalized solution of the inconsistent fuzzy linear system involving the core-EP inverse of an associated matrix. Before this can be achieved, it is necessary to study the block structure of the core-EP inverse. Finally, results are illustrated with some numerical examples.

In this note, we give necessary and sufficient conditions for which the absorption laws and the reverse order laws of two kinds of generalized core inverses hold.

In this article, we study the existence criterion and formulae of Drazin inverses of elements in a certain finite-dimensional algebra generated by two idempotents, under some prescribed conditions.