Additive properties and absorption laws for generalized inverses
Abstract
Let a, f be elements in a ring with pseudo core inverses a◯D, f◯D, and let b = f−a. We prove that the absorption law a◯D(a+f)f◯D=a◯D+f◯D holds if and only if 1+a◯Db is invertible and the additive property f◯D=(1+a◯Db)−1a◯D is satisfied. We further characterize these properties and establish analogous results for other generalized inverses. Finally, we apply these results to the case of complex matrices.
Fields of Study & Subjects
Matrix Theory and Algorithms
Numerical methods in inverse problems
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Linear and Multilinear Algebra
- Publisher
- Informa UK Limited
- Volume
- 74
- Issue
- 2
- Pages
- 213–227
- Publication date
- 7 January 2026
- Language
- EN