The Sherman–Morrison–Woodbury formula for the Moore–Penrose metric generalized inverse

DOI10.1080/03081087.2018.1523863zbMath1459.15008OpenAlexW2890232279WikidataQ114641384 ScholiaQ114641384MaRDI QIDQ5145549

Jian Bing Cao, Dongwei Shi

Publication date: 21 January 2021

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2018.1523863

zbMATH Keywords

perturbationBanach spaceMoore-Penrose inverseSherman-Morrison-Woodbury formulametric generalized inverse

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbation analysis for the Moore-Penrose metric generalized inverse of closed linear operators in Banach spaces
• Perturbation of the Moore-Penrose metric generalized inverse in reflexive strictly convex Banach spaces
• Outcome space range reduction method for global optimization of sum of affine ratios problem
• Perturbations of Moore-Penrose metric generalized inverses of linear operators in Banach spaces
• A generalization of the Sherman-Morrison-Woodbury formula
• The best generalised inverse of the linear operator in normed linear space
• A spectrum theorem for perturbed bounded linear operators
• On the expression of generalized inverses of perturbed bounded linear operators
• A revisitation of formulae for the Moore-Penrose inverse of modified matrices.
• Metric generalized inverse of linear operator in Banach space
• Criteria for the metric generalized inverse and its selections in Banach spaces
• Perturbation analysis of bounded homogeneous generalized inverses on Banach spaces
• An Operator Pseudo-Inversion Lemma
• Updating the Inverse of a Matrix
• A Sherman–Morrison–Woodbury Identity for Rank Augmenting Matrices with Application to Centering
• An Efficient Algorithm for Quadratic Sum-of-Ratios Fractional Programs Problem
• Perturbation Analysis of the Algebraic Metric Generalized Inverse in L^p(Ω,μ)
• Generalized Inversion of Modified Matrices
• Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix

This page was built for publication: The Sherman–Morrison–Woodbury formula for the Moore–Penrose metric generalized inverse