Idempotent operator and its applications in Schur complements on Hilbert \(C^*\)-module

DOI10.1515/spma-2022-0187MaRDI QIDQ6172906

Z. Niazi Moghani, Mehdi Mohammadzadeh Karizaki

Publication date: 20 July 2023

Published in: Special Matrices (Search for Journal in Brave)

zbMATH Keywords

Moore-Penrose inverseSchur complementsidempotent operator

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Cites Work

• Unnamed Item
• Commuting \(C^*\) modular operators
• Group rings in which every element is uniquely the sum of a unit and an idempotent.
• What are Schur complements, anyway?
• Schur complements and statistics
• Properties of Schur complements in partitioned idempotent matrices.
• Inverses of \(2\times 2\) block matrices
• Manifestations of the Schur complement
• Block idempotent matrices and generalized Schur complement
• Positive semi-definite matrices of adjointable operators on Hilbert \(C^{*}\)-modules
• Determination of the inertia of a partitioned Hermitian matrix
• RANGE PROJECTIONS OF IDEMPOTENTS IN C*-ALGEBRAS
• Some regular sums
• Updating the Inverse of a Matrix
• Idempotent Elements in a Bernstein Algebra
• Conditions that the product of operators is an EP operator in Hilbert C*-module
• Operator matrix of Moore–Penrose inverse operators on Hilbert C^*-modules
• Moore-Penrose inverse of product operators in Hilbert C*- modules
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses

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