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.

Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of adL. For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. The constructi...

We give a generalization of the Penrose transform on Hermitian manifolds with metrics locally conformally equivalent to Bochner-Kähler metrics. We also give an explicit formula for the inverse transform. 1991 Mathematics Subject Classification: 32L25 (Primary), 53C55, 32C35 (Secondary)

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.