Moore-Penrose inverse, generalized Schur complement and inertia
Abstract
Abstract In this article, a generalized Schur complement defined by the Moore-Penrose inverse and *congruence to a Hermitian block matrix are studied for a generalization of Haynsworth’s theorem. As an application, an alternative proof of Albert’s characterization of positivity is obtained [A. Albert, SIAM J. Appl. Math. (1969)]. Some of our results of matrices are extended to bounded linear operators.
Fields of Study & Subjects
Matrix Theory and Algorithms
Mathematical Inequalities and Applications
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Acta Scientiarum Mathematicarum
- Publication date
- 27 February 2026
- Language
- EN