Solutions to optimization problems on ranks and inertias of a matrix function with applications

DOI10.1016/j.amc.2012.09.024zbMath1309.15025OpenAlexW2126111612MaRDI QIDQ2018984

Zhuo-Heng He, Qing-Wen Wang

Publication date: 26 March 2015

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.09.024

zbMATH Keywords

rankinertiaMoore-Penrose inversematrix equationre-nonnegative semidefinite matrix

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (8)

Ranks of a constrained Hermitian matrix expression with applications ⋮ Solving optimization problems on Hermitian matrix functions with applications ⋮ The optimization on ranks and inertias of a quadratic Hermitian matrix function and its applications ⋮ The general solutions to some systems of matrix equations ⋮ A system of matrix equations and its applications ⋮ The consistency and the exact solutions to a system of matrix equations ⋮ The complete equivalence canonical form of four matrices over an arbitrary division ring ⋮ Characterization for the general solution to a system of matrix equations with quadruple variables

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The common bisymmetric nonnegative definite solutions with extreme ranks and inertias to a pair of matrix equations
• Inertias and ranks of some Hermitian matrix functions with applications
• On the Hermitian solutions to a system of adjointable operator equations
• Max-min problems on the ranks and inertias of the matrix expressions \(A - BXC \pm (BXC)^{\ast}\) with applications
• An equivalence canonical form of a matrix triplet over an arbitrary division ring with applications
• Maximization and minimization of the rank and inertia of the Hermitian matrix expression \(A-BX-(BX)^{*}\) with applications
• The common positive solution to adjointable operator equations with an application
• The general coupled matrix equations over generalized bisymmetric matrices
• The common solution to matrix equations over a regular ring with applications
• Explicit solution of the operator equation \(A^{*}X+X^{*}A=B\)
• On the existence of Hermitian positive definite solutions of the matrix equation \(X^s+A^*X^{-t}A=Q\)
• The solutions to some operator equations
• Common Hermitian solutions to some operator equations on Hilbert \(C^{*}\)-modules
• Ranks and the least-norm of the general solution to a system of quaternion matrix equations
• A system of real quaternion matrix equations with applications
• Minimum norm regularization of descriptor systems by mixed output feedback
• The Re-positive definite solutions to the matrix inverse problem \(AX = B\)
• On solvents of matrix polynomials.
• The Sylvester equation and approximate balanced reduction
• The solution to matrix equation \(AX+X^TC=B\)
• Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application
• The common solution to six quaternion matrix equations with applications
• \(P\)-(skew)symmetric common solutions to a pair of quaternion matrix equations
• Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications
• A system of matrix equations over regular rings
• A system of four matrix equations over von Neumann regular rings and its applications
• A simultaneous decomposition of a matrix triplet with applications
• A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications
• The general solution to a system of adjointable operator equations over Hilbert C^∗-modules
• Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation
• Some matrix equations with applications†
• Re-nnd SOLUTIONS OF THE MATRIX EQUATION AXB=C
• Extreme Ranks of Real Matrices in Solution of the Quaternion Matrix Equation AXB = C with Applications
• A new solvable condition for a pair of generalized Sylvester equations
• Inertia and Rank Characterizations of Some Matrix Expressions
• Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications
• The Equations A^TX\pm X^TA=B
• Regularization of Singular Systems by Derivative and Proportional Output Feedback
• Extremal Ranks of Some Symmetric Matrix Expressions with Applications
• A real quaternion matrix equation with applications
• The Real Solutions to a System of Quaternion Matrix Equations with Applications
• On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity
• Positive solutions to a system of adjointable operator equations over Hilbert \(C^*\)-modules

This page was built for publication: Solutions to optimization problems on ranks and inertias of a matrix function with applications