C. Mendes Araújo

Moore–Penrose invertibility in involutory rings: the case aa †=bb †

In this article, we consider Moore–Penrose invertibility in rings with a general involution. Given two von Neumann regular elements a, b in a general ring with an arbitrary involution, we aim to give necessary and sufficient conditions to aa † = bb †. As a special case, EP elements are considered.

N-matrix completion problem

Abstract An n×n matrix is called an N-matrix if all principal minors are negative. In this paper, we are interested in N-matrix completion problems, that is, when a partial N-matrix has an N-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N-matrix does not have an N-matrix completion. Here we prove that a combinatorially symmetric partial N-matrix has an N-matrix completion if the graph of its specified entries is a 1-chordal graph. We also prove that there exists an N-matrix completion for a partial N-matrix whose associated graph is an undirected cycle.