The consistency and the exact solutions to a system of matrix equations

DOI10.1080/03081087.2016.1140717zbMath1357.15007OpenAlexW2306444147MaRDI QIDQ2953175

Qing-Wen Wang, F. O. Farid, Zhuo-Heng He

Publication date: 3 January 2017

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

Full work available at URL: https://doi.org/10.1080/03081087.2016.1140717

zbMATH Keywords

rankinertiageneralized inversesMoore-Penrose inversesystem of matrix equations

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (6)

A constraint system of generalized Sylvester quaternion matrix equations ⋮ The relaxed gradient based iterative algorithm for solving matrix equations \(A_iXB_i=F_i\) ⋮ A System of Periodic Discrete-time Coupled Sylvester Quaternion Matrix Equations ⋮ Determinantal representations of solutions and Hermitian solutions to some system of two-sided quaternion matrix equations ⋮ Simultaneous decomposition of quaternion matrices involving \(\eta\)-Hermicity with applications ⋮ Cramer's rules for Sylvester quaternion matrix equation and its special cases

Cites Work

• On the Hermitian solutions to a system of adjointable operator equations
• Minimal ranks of some quaternion matrix expressions with applications
• Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra
• Some matrix equations over a finite field
• Explicit solution of the operator equation \(A^{*}X+X^{*}A=B\)
• On solutions of the quaternion matrix equation \(AX=B\) and their applications in color image restoration
• A pair of simultaneous linear matrix equations \(A_ 1XB_ 1=C_ 1,A_ 2XB_ 2=C_ 2\) and a matrix programming problem
• The solutions to some operator equations
• Common Hermitian solutions to some operator equations on Hilbert \(C^{*}\)-modules
• A system of real quaternion matrix equations with applications
• The matrix equation AXB+CYD=E
• Inertia and biclique decompositions of joins of graphs
• Solutions to optimization problems on ranks and inertias of a matrix function with applications
• Positive solutions to the equations \(AX=C\) and \(XB=D\) for Hilbert space operators
• The solvability of two linear matrix equations
• Extreme ranks of (skew-)Hermitian solutions to a quaternion matrix equation
• Some matrix equations with applications†
• A new solvable condition for a pair of generalized Sylvester equations
• Inertia and Rank Characterizations of Some Matrix Expressions
• Matrix Analysis
• Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
• Consistency of a pair of generalized Sylvester equations
• A real quaternion matrix equation with applications
• Positive and real-positive solutions to the equationaxa*=cinC*-algebras

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