Ranks of Hermitian and skew-Hermitian solutions to the matrix equation \(AXA^*=B\)

DOI10.1016/j.laa.2009.03.011zbMath1180.15018OpenAlexW2028242709MaRDI QIDQ1039745

Yoshio Takane, Yongge Tian, Yong Hui Liu

Publication date: 23 November 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.2009.03.011

zbMATH Keywords

generalized inversesolvability conditionsminimal rankmaximal rankHermitian solutioncomplex matrix equationsskew-Hermitian solution

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Hermitian, skew-Hermitian, and related matrices (15B57) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (23)

A simultaneous decomposition of a matrix triplet with applications ⋮ The generalized conjugate direction method for solving quadratic inverse eigenvalue problems over generalized skew Hamiltonian matrices with a submatrix constraint ⋮ Ranks of a constrained Hermitian matrix expression with applications ⋮ Least-squares solutions and least-rank solutions of the matrix equation AXA ^*  = B and their relations ⋮ Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions ⋮ A system of matrix equations and its applications ⋮ Solutions to 18 constrained optimization problems on the rank and inertia of the linear matrix function ⋮ Solvability of systems of linear matrix equations subject to a matrix inequality ⋮ Submatrix constrained least-squares inverse problem for symmetric matrices from the design of vibrating structures ⋮ The anti-symmetric solution of the matrix equation \(AXA^{\top} =B\) on a null subspace ⋮ On additive decomposition of the Hermitian solution of the matrix equation \(AXA^* = B\) ⋮ The real and complex Hermitian solutions to a system of quaternion matrix equations with applications ⋮ Maximization and minimization of the rank and inertia of the Hermitian matrix expression \(A-BX-(BX)^{*}\) with applications ⋮ Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method ⋮ On solvability of Hermitian solutions to a system of five matrix equations ⋮ Common Hermitian least squares solutions of matrix equations \(A_1XA^*_1=B_1\) and \(A_2XA^*_2=B_2\) subject to inequality restrictions ⋮ Extremal ranks of some nonlinear matrix expressions with applications ⋮ Hermitian‐type generalized singular value decomposition with applications ⋮ A survey on rank and inertia optimization problems of the matrix-valued function \(A+BXB^\ast\) ⋮ Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices ⋮ Algorithm for inequality-constrained least squares problems ⋮ Max-min problems on the ranks and inertias of the matrix expressions \(A - BXC \pm (BXC)^{\ast}\) with applications ⋮ Ranks of submatrices in (skew-)Hermitian solutions to a quaternion matrix equation

Cites Work

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• THREE RANK FORMULAS ASSOCIATED WITH THE COVARIANCE MATRICES OF THE BLUE AND THE OLSE IN THE GENERAL LINEAR MODEL

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