The general common Hermitian nonnegative-definite solution to the matrix equations \(AXA=BB\) and \(CXC=DD\) with applications in statistics

DOI10.1016/j.jmva.2004.04.009zbMath1071.15014OpenAlexW2056008400MaRDI QIDQ1776870

Xian Zhang

Publication date: 12 May 2005

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2004.04.009

zbMATH Keywords

regressionmatrix equationMoore-Penrose generalized inversemultivariate linear modellinear hypothesiscolumn spaceHermitian (symmetric) nonnegative-definite solutionHermitian (symmetric) positive-definite solutionkernel space

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Hypothesis testing in multivariate analysis (62H15) Matrix equations and identities (15A24) Factorial statistical designs (62K15)

Related Items (13)

The common re-nonnegative definite and re-positive definite solutions to the matrix equations \(A_1XA_1^\ast = C_1\) and \(A_2XA_2^\ast = C_2 \) ⋮ A Hermitian least squares solution of the matrix equation \(AXB=C\) subject to inequality restrictions ⋮ Least-squares solutions and least-rank solutions of the matrix equation AXA ^*  = B and their relations ⋮ Extremal ranks of matrix expression of \(A - BXC\) with respect to Hermitian matrix ⋮ Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions ⋮ Common Hermitian least squares solutions of matrix equations \(A_1XA^*_1=B_1\) and \(A_2XA^*_2=B_2\) subject to inequality restrictions ⋮ The Hermitian solution of \(A X A^* = B\) subject to \(CXC^{*} \geq D\) ⋮ Characterizations of noncentral chi-squared-generating covariance structures for a normally distributed random vector ⋮ On the invertibility of the operatorA-XB ⋮ Positive and real-positive solutions to the equationaxa*=cinC*-algebras ⋮ Common nonnegative definite solutions of some classical matrix equations ⋮ On Hermitian nonnegative-definite solutions to matrix equations ⋮ Nonnegative definite and re-nonnegative definite solutions to a system of matrix equations with statistical applications

Cites Work

• Independence distribution preserving covariance structures for the multivariate linear model
• The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation \(AXA^{\ast}=B\)
• Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
• Linear matrix equations from an inverse problem of vibration theory
• Nonnegative definite and positive definite solutions to the matrix equationAXA^*=B
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• When Does Rank(A+B)=Rank(A)+Rank(B)?
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