Some inequalities on generalized Schur complements

DOI10.1016/S0024-3795(99)00071-3zbMath0947.15010MaRDI QIDQ1970437

Fuzhen Zhang, Xiuping Zhang, Bo Ying Wang

Publication date: 7 November 2000

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

zbMATH Keywords

inequalitieseigenvaluesgeneralized inversepositive semidefinite matricesMoore-Penrose pseudoinversegeneralized Schur complement

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Inequalities involving eigenvalues and eigenvectors (15A42)

Related Items (8)

A matrix inequality on Schur complements ⋮ A Matrix Identity on the Schur Complement ⋮ Generalized Schur complements involving the Kronecker products of positive semidefinite matrices ⋮ On generalized Schur complement of matrices and its applications to real and integer matrix factorizations ⋮ Expression of the Drazin and MP-inverse of partitioned matrix and quotient identity of generalized Schur complement ⋮ The Schur complements of generalized doubly diagonally dominant matrices ⋮ Two inequalities involving Hadamard products of positive semi-definite Hermitian matrices ⋮ The equivalent form of a matrix inequality and its application

Cites Work

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• Six generalized Schur complements
• Some interlacing properties of the Schur complement of a Hermitian matrix
• Generalized Schur complements
• Manifestations of the Schur complement
• Determination of the inertia of a partitioned Hermitian matrix
• Reduction of a matrix using properties of the Schur complement
• Matrix Analysis
• Schur complements and matrix inequalities of hadamard products^∗
• Trace and Eigenvalue Inequalities for Ordinary and Hadamard Products of Positive Semidefinite Hermitian Matrices
• Applications of an Inequality for the Schur Complement
• A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
• Matrix theory. Basic results and techniques

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