On the binary relations defined using GD1 and 1GD inverses over infinite dimensional vector spaces
Year: 2026
Type: preprint
Abstract: The purpose of this article is to study certain binary relations of endomorphisms over infinite dimensional vector spaces defined by GD1 and 1GD generalized inverses. In order to do so, these generalized inverses are studied over arbitrary vector spaces (namely, infinite dimensional ones) using finite potent endomorphisms. We characterize them in terms of the AST decomposition of a finite potent endomorphism and we obtain algorithms for their respective computation. This theory is then used to characterize the GD1 and 1GD binary relations for finite potent endomorphisms in terms of the AST decomposition and to prove that they define partial orders in the set of finite potent endomorphisms, thus, completing the theory of these generalized inverses for matrices.
Source: arXiv (Cornell University)
Institution: University of Castilla-La Mancha
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Agencia Estatal de Investigación
Awards: G464105488, G6048790067
OpenAlex ID: W7158635833
Cites:
Cited by:
Related to: