In this paper, we present characterizations for the level-2 condition number of the weighted Moore–Penrose inverse, i.e., condMN (A) ≤ cond [2] MN (A) ≤ condMN (A)+ 1, where condMN (A) is the condition number of the weighted Moore–Penrose inverse of a rectangular matrix and cond [2] MN (A) is the level-2 condition number of this problem. This paper extends the result by Cucker, Diao and Wei [F....

The Moore-Penrose inverse of a real matrix having no square submatrix with two or more diagonals is described in terms of bipartite graphs. For such a matrix, the sign of every entry of the Moore-Penrose inverse is shown to be determined uniquely by the signs of the matrix entries; i.e., the matrix has a signed generalized inverse. Necessary and sufficient conditions on an acyclic bipartite gra...

In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m× n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.

In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m× n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.

We present some equivalent conditions of the reverse order law for the Moore–Penrose inverse in rings with involution, extending some well-known results to more general settings. Then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted Moore-Penrose inverse in C∗-algebras.

In this paper, we study representations of the Moore-Penrose inverse of a 2 × 2 matrix M over a ∗-regular ring with two term star-cancellation. As applications, some necessary and sufficient conditions for the Moore-Penrose inverse of M to have different types are given.

We investigate necessary and sufficient conditions for aae,f = bb † e,f to hold in rings with involution. Here, ae,f denotes the weighted Moore-Penrose inverse of a, related to invertible and Hermitian elements e, f ∈ R. Thus, some recent results from [7] are extended to the weighted Moore-Penrose inverse.