Recent Advances in Matrix Generalized Inverses and Applications
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".
Deadline for manuscript submissions: 31 December 2025 | Viewed by 40
Special Issue Editor
Interests: generalized inverses; matrix analysis; linear and multilinear algebra; operator matrices; matrix theory; functional analysis; approximation theory
Special Issue Information
Dear Colleagues,
The theory of generalized inverses forms a cornerstone of modern matrix analysis, with deep connections to operator theory, numerical linear algebra, and a wide array of applications in pure and applied mathematics. Since the early 2010s, numerous new classes of generalized inverses have been introduced and studied within diverse structural and algebraic frameworks, including the core inverse, the inverse along an element, and the (b,c)-Drazin inverse. Subsequent developments have led to further extensions of the core inverse—such as the DMP, core-EP, BT, and WC inverses—as well as alternative generalizations of the group inverse, including the weak group inverse, the generalized group inverse, and, more generally, the m-weak group and m-weak core inverses.
In parallel, various partial orders and pre-orders have been proposed to reflect the intrinsic algebraic and geometric structures underpinning these inverses. Notable examples include the core partial order and the core-EP pre-order induced by the core and core-EP inverses, respectively.
These advances have significantly enhanced our understanding of matrix and operator equations, perturbation theory, and induced matrix order relations.
This Special Issue in Axioms aims to gather recent contributions on the theory, computation, and applications of generalized inverses, matrix orderings, and their extensions to broader algebraic contexts, including operators on Banach and Hilbert spaces, rings, C*-algebras, and tensors. Topics of interest include, but are not limited to:
- New classes of generalized inverses
- New partial and pre-orders in matrix and operator theory
- Iterative methods and perturbation analysis for generalized inverses
- Matrix equations over fields, quaternions, and tensors involving generalized inverses
- Extensions of matrix concepts to rings, algebras, and infinite-dimensional settings
We welcome original research articles and review papers addressing theoretical advances, computational approaches, and interdisciplinary applications.
Prof. Dr. David E. Ferreyra
Guest Editor
Manuscript Submission Information
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Keywords
- generalized inverses
- matrix partial orders
- operator and quaternion equations
- matrix and tensor equations
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