An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4}-inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A{2, 3}s and A{2, 4}s are characterized in terms of matrix products (R∗A)†R∗ and T ∗(AT ∗)†, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representat...

In this paper we give a representation of the Moore-Penrose inverse of a linear combination of generalized and hypergeneralized projectors. Also, we consider the invertibility of some linear combination of commuting generalized and hypergeneralized projectors.

In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for different scientists dealing with optimization problems, data analysis, solutions of linear integral equations, etc. At first we will present a review of some of the basic results on the so-called Moore-Penrose pseudoinverse of matrices, a concept that...

In this paper, we obtain optimal perturbation bounds of the weighted Moore-Penrose inverse under the weighted unitary invariant norm, the weighted Q-norm and the weighted F -norm, and thereby extend some recent results.

In this paper, some new representations of the Moore-Penrose inverse of a complex m × n matrix of rank r in terms of (s × t)-constrained submatrices with m ≥ s ≥ r, n ≥ t ≥ r are presented.

In this paper, we obtain optimal perturbation bounds of the weighted Moore-Penrose inverse under the weighted unitary invariant norm, the weighted Q-norm and the weighted F -norm, and thereby extend some recent results.

In this paper, we investigate the Sherman-Morrison-Woodbury formula for {1}-inverses and {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A+YGZ*)? = A? ?A?Y(G? +Z*A?Y)?Z*A? holds, where stands any kind standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose Drazin group core inverse dual A.

Closed-form formulas are derived for the rank and inertia of submatrices of the Moore–Penrose inverse of a Hermitian matrix. A variety of consequences on the nonsingularity, nullity and definiteness of the submatrices are also presented.

After decades studying extensively two generalized inverses, namely Moore--Penrose inverse and Drazin inverse, currently, we found immersed in a new generation of inverses (core DMP etc.). The main aim this paper is to introduce investigate matrix related these defined for rectangular matrices. We apply our results the solution linear systems.