Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities

DOI10.1007/BF02227445zbMath0723.15017OpenAlexW2029459936MaRDI QIDQ757544

Simo Puntanen, Jerzy K. Baksalary

Publication date: 1991

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/137396

zbMATH Keywords

Moore-Penrose inversesKantorovich inequalitypositive semidefinite matricesCauchy-Schwarz inequalitymatrix versions

Mathematics Subject Classification ID

Miscellaneous inequalities involving matrices (15A45) Inequalities for sums, series and integrals (26D15)

Related Items (16)

Certain integral inequalities involving tensor products, positive linear maps, and operator means ⋮ A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition ⋮ An extension of the operator Kantorovich inequality ⋮ Kantorovich and Cauchy-Schwarz inequalities involving positive semidefinite matrices, and efficiency comparisons for a singular linear model ⋮ Equality conditions for matrix Kantorovich-type inequalities ⋮ Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor ⋮ Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications ⋮ Matrix Euclidean norm Wielandt inequalities and their applications to statistics ⋮ Refinements of Kantorovich inequality for Hermitian matrices ⋮ GENERALIZED KANTOROVICH CONSTANT, A NEW FORMULATION AND PROPERTIES ⋮ Bounds for the trace of the difference of the covariance matrices of the OLSE and BLUE ⋮ Constrained Kantorovich inequalities and relative efficiency of least squares ⋮ Operator versions of the Kantorovich inequality ⋮ A survey of Cauchy-Schwarz and Kantorovich-type matrix inequalities ⋮ Kantorovich-type inequalities for operators via \(D\)-optimal design theory ⋮ A converse to the Jensen inequality, its matrix extensions and inequalities for minors and eigenvalues

Cites Work

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• Matrix versions of the Cauchy and Kantorovich inequalities
• The matrix inequality \(M \leq B^*MB\)
• Reserval of the Lyapunov, Hölder, and Minkowski inequalities and other extensions of the Kantorovich inequality
• On principal submatrices
• Optimum properties of latin square designs and a matrix inequality
• Relationships Between Some Representations of the Best Linear Unbiased Estimator in the General Gauss–Markoff Model
• On Least Squares with Insufficient Observations
• Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters
• An Extension of the Generalized Inverse of a Matrix
• A remark on the preceding paper

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