Further inequalities involving the Khatri-Rao product

DOI10.1016/j.laa.2008.12.004zbMath1179.15022OpenAlexW1976790778MaRDI QIDQ1017630

Shuangzhe Liu, Götz Trenkler, Zhong-Peng Yang

Publication date: 12 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.12.004

zbMATH Keywords

Schur complementHadamard productmatrix inequalitiesKronecker productpositive definite matrixKantorovich-type inequalitiesKhatri-Rao productnon-singular Hermitian matricesTracy-Singh product

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Miscellaneous inequalities involving matrices (15A45) Multilinear algebra, tensor calculus (15A69)

Related Items

The further generalization on the inequalities for Hadamard products of any number of invertible Hermitian matrices ⋮ Matrix derivatives and Kronecker products for the core and generalized core inverses ⋮ Matrix differential calculus with applications in the multivariate linear model and its diagnostics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Block Kronecker products and the vecb operator
• Concavity of certain maps on positive definite matrices and applications to Hadamard products
• Equality conditions for matrix Kantorovich-type inequalities
• Schur complements and matrix inequalities in the Löwner ordering
• The Schur complement and its applications
• Several inequalities involving Khatri-Rao products of positive semidefinite matrices
• A quantitative version of the observation that the Hadamard product is a principal submatrix of the Kronecker product
• Inequalities involving Hadamard products of positive semidefinite matrices
• Hadamard products and multivariate statistical analysis
• A new matrix product and its applications in partitioned matrix differentiation