The matrix inequality \(M \leq B^*MB\)

DOI10.1016/0024-3795(83)90206-9zbMath0516.15010OpenAlexW2068949655MaRDI QIDQ1052427

K. Klaczynski, Jerzy K. Baksalary, Radosław Kala

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0024-3795(83)90206-9

zbMATH Keywords

matrix inequalitypartial orderingsLoewner partial orderingDrazin partial orderingnonnegative definite Hermitian matricesrank subtractivity partial ordering

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Miscellaneous inequalities involving matrices (15A45) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (14)

On some characterizations of the star partial ordering for matrices and rank subtractivity ⋮ The positive semidefiniteness of partitioned matrices ⋮ Restricted minimax estimation in semiparametric linear models ⋮ Some further aspects of the löwner-ordering antitonicity of the moore-penrose inverse ⋮ Characterizations of the best linear unbiased estimator in the general Gauss-Markov model with the use of matrix partial orderings ⋮ Characterizations and dispersion-matrix robustness of efficiently estimable parametric functionals in linear models with nuisance parameters ⋮ On the Löwner, minus, and star partial orderings of nonnegative definite matrices and their squares ⋮ Some further results on Hermitian-matrix inequalities ⋮ Löwner partial ordering and space preordering of Hermitian non-negative definite matrices ⋮ Equalities and inequalities for inertias of Hermitian matrices with applications ⋮ Two local operators and the BLUE ⋮ Dispersion-diminishing transformations ⋮ Spectrum and trace invariance criterion and its statistical applications ⋮ Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities

Cites Work

• Prior Information on the Coefficients when the Disturbance Covariance Matrix is Unknown
• Optimum properties of latin square designs and a matrix inequality
• Natural structures on semigroups with involution
• A note on the partial ordering of positive semi-definite matrices
• On Canonical Forms, Non-Negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models
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