Generalization of Roth's solvability criteria to systems of matrix equations

DOI10.1016/j.laa.2017.04.011zbMath1365.15020arXiv1704.04670OpenAlexW2606044292MaRDI QIDQ2359568

Vladimir V. Sergeichuk, Tetiana Klymchuk, Andrii Dmytryshyn, Vyacheslav M. Futorny

Publication date: 22 June 2017

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

Full work available at URL: https://arxiv.org/abs/1704.04670

zbMATH Keywords

Sylvester equationssystems of matrix equationsRoth's criteria

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Related Items (12)

A real representation of complex polynomial matrices in the framework of conjugate product ⋮ On the solvability of generalized Sylvester operator equations ⋮ A system of Sylvester-type quaternion matrix equations with ten variables ⋮ The solutions of the quaternion matrix equation \(AX^\varepsilon + BX^\delta = 0\) ⋮ A system of coupled quaternion matrix equations with seven unknowns and its applications ⋮ Tensor form of GPBiCG algorithm for solving the generalized Sylvester quaternion tensor equations ⋮ On the generalized Sylvester operator equation AX − Y B  =  C ⋮ A system of quaternary coupled Sylvester-type real quaternion matrix equations ⋮ Least squares solution of the quaternion Sylvester tensor equation ⋮ Determinantal representations of the solutions to systems of generalized Sylvester equations ⋮ Least-norm of the general solution to some system of quaternion matrix equations and its determinantal representations ⋮ Explicit formulas and determinantal representation for η-skew-Hermitian solution to a system of quaternion matrix equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complex conjugate matrix equations for systems and control
• Roth's solvability criteria for the matrix equations \(AX-\hat{X}B=C\) and \(X-A\hat{X}B=C\) over the skew field of quaternions with an involutive automorphism \(q \mapsto \hat{q}\)
• Inertia characteristics of self-adjoint matrix polynomials
• Roth's theorems for matrix equations with symmetry constraints
• Consimilarity and quaternion matrix equations \(AX -\hat{X}B = C\), \(X - A\hat{X}B = C\)
• Computational Methods for Linear Matrix Equations
• The Matrix Equation $A\bar X - XB = C$ and Its Special Cases
• On the matrix equations $AX - XB = C$ and $AX - YB = C$
• Consistency of a pair of generalized Sylvester equations
• Generalized Sylvester Equations
• Coupled Sylvester-type Matrix Equations and Block Diagonalization
• The Equations AX - YB = C and AX - XB = C in Matrices

This page was built for publication: Generalization of Roth's solvability criteria to systems of matrix equations