The general common nonnegative-definite and positive-definite solutions to the matrix equations \(AXA^ *=BB^ *\) and \(CXC^ *=DD^ *\).

DOI10.1016/S0893-9659(04)90123-1zbMath1062.15009OpenAlexW1992201645MaRDI QIDQ1764554

Xian Zhang, Mei-yu Cheng

Publication date: 25 February 2005

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(04)90123-1

zbMATH Keywords

generalized inversepair of matrix equationsnullspacecolumn spacenonnegative-definite solutionpositive-definite solution

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Related Items (9)

The common re-nonnegative definite and re-positive definite solutions to the matrix equations \(A_1XA_1^\ast = C_1\) and \(A_2XA_2^\ast = C_2 \) ⋮ Unnamed Item ⋮ Least-squares solutions and least-rank solutions of the matrix equation AXA ^*  = B and their relations ⋮ Finite iterative algorithms for a common solution to a group of complex matrix equations ⋮ On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity ⋮ Positive and real-positive solutions to the equationaxa*=cinC*-algebras ⋮ Common nonnegative definite solutions of some classical matrix equations ⋮ The *congruence class of the solutions of some matrix equations ⋮ Nonnegative definite and re-nonnegative definite solutions to a system of matrix equations with statistical applications

Cites Work

• Unnamed Item
• Unnamed Item
• 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)?

This page was built for publication: The general common nonnegative-definite and positive-definite solutions to the matrix equations \(AXA^ *=BB^ *\) and \(CXC^ *=DD^ *\).