Several inequalities involving Khatri-Rao products of positive semidefinite matrices

DOI10.1016/S0024-3795(02)00338-5zbMath1016.15016MaRDI QIDQ1855352

Shuangzhe Liu

Publication date: 5 February 2003

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

zbMATH Keywords

Hadamard productmatrix inequalityMoore-Penrose inverseKronecker productpositive semidefinite matricesKhatri-Rao productTracy-Singh product

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Miscellaneous inequalities involving matrices (15A45)

Related Items (11)

Vector least-squares solutions for coupled singular matrix equations ⋮ Several Kantorovich Inequalities Involving Tracy-Singh Product ⋮ RETRACTED: The general (vector) solutions of such linear (coupled) matrix fractional differential equations by using Kronecker structures ⋮ Schur's theorem for a block Hadamard product ⋮ Khatri-Rao products for operator matrices acting on the direct sum of Hilbert spaces ⋮ Some new connections between matrix products for partitioned and non-partitioned matrices ⋮ Extension and generalization inequalities involving the Khatri-Rao product of several ⋮ A Perron-Frobenius theory for block matrices associated to a multiplex network ⋮ Further inequalities involving the Khatri-Rao product ⋮ An Oppenheim type determinantal inequality for the Khatri-Rao product ⋮ The equivalent form of a matrix inequality and its application

Cites Work

• Block Kronecker products and the vecb operator
• A matrix version of the Wielandt inequality and its applications to 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
• Matrix results on the Khatri-Rao and Tracy-Singh products
• Majorizations of Hadamard products of matrix powers
• Several matrix Kantorovich-type inequalities
• A quantitative version of the observation that the Hadamard product is a principal submatrix of the Kronecker product
• Hadamard products and multivariate statistical analysis
• On hsu's model in regression analysis
• Schur complements and matrix inequalities of hadamard products^∗
• Inequalities for the Hadamard Product of Matrices
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
• A new matrix product and its applications in partitioned matrix differentiation
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