Schur complements and matrix inequalities in the Löwner ordering

DOI10.1016/S0024-3795(00)00032-XzbMath0977.15008MaRDI QIDQ1595165

Fuzhen Zhang

Publication date: 28 January 2002

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

zbMATH Keywords

Schur complementHadamard productLöwner partial orderingmatrix inequalityKronecker product

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45) Multilinear algebra, tensor calculus (15A69)

Related Items (8)

A Matrix Identity on the Schur Complement ⋮ The further generalization on the inequalities for Hadamard products of any number of invertible Hermitian matrices ⋮ Some new connections between matrix products for partitioned and non-partitioned matrices ⋮ C*-algebraic Schur product theorem, P\'{o}lya-Szeg\H{o}-Rudin question and Novak's conjecture ⋮ Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models ⋮ On some matrix trace inequalities ⋮ Further inequalities involving the Khatri-Rao product ⋮ The Schur complements of generalized doubly diagonally dominant matrices

Cites Work

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• Cauchy-Schwarz inequalities associated with positive semidefinite matrices
• A generalization of \(A\circ A^{-1}\geq I\)
• Schur complements and statistics
• Concavity of certain maps on positive definite matrices and applications to Hadamard products
• Block-matrix generalizations of Schur's basic theorems on Hadamard products
• Manifestations of the Schur complement
• A quantitative version of the observation that the Hadamard product is a principal submatrix of the Kronecker product
• Some operator inequalities of the Schwarz type
• Hadamard products and multivariate statistical analysis
• A Note on the Hadamard Product
• Über eine Ungleichung für positiv definite Matrizen
• An Application of Theorems of Schur and Albert
• Partitioned and Hadamard product matrix inequalities
• Schur complements and matrix inequalities of hadamard products^∗
• Notes on hadamard products of matrices
• Applications of an Inequality for the Schur Complement
• An Inequality for Linear Transformations
• Inequalities: theory of majorization and its applications
• Matrix theory. Basic results and techniques

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