With respect to the Dirac operator and the conformally invariant Laplacian, an explicit description of the inverse Penrose transform on Riemannian twistor spaces is given. A Dolbeault representative of cohomology on the twistor space is constructed from a solution of the field equation on the base manifold.

We study the spectrum and the rank of a linear combination of two orthogonal projectors. We characterize when this linear combination is EP, diagonalizable, idempotent, tripotent, involutive, nilpotent, generalized projector, and hypergeneralized projector. Also we derive the Moore-Penrose inverse of a linear combination of two orthogonal projectors in a particular case. The main tool used here...

We modify the algorithm of [1], based on Newton’s iteration and on the concept of 2-displacement rank, to the computation of the Moore-Penrose inverse of a rank-deficient Toeplitz matrix. Numerical results are presented to illustrate the effectiveness of the method.

Let A be a nonnegative idempotent matrix. It is shown that the Schur complement of a submatrix, using the Moore-Penrose inverse, is a nonnegative idempotent matrix if the submatrix has a positive diagonal. Similar results for the Schur complement of any submatrix of A are no longer true in general.