Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra

DOI10.1016/S0024-3795(02)00303-8zbMath1004.15017MaRDI QIDQ697052

Qing-Wen Wang, Shang-Zhi Li, Jian-Hua Sun

Publication date: 12 September 2002

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

zbMATH Keywords

consistencyregular matrix pencil(skew) selfconjugate matrixcentral algebracentro (skew) symmetric matrixper (skew) selfconjugate matrixregular matrix quadruplesystem of generalized Sylvester equations

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24)

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Cites Work

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• Roth's theorems for sets of matrices
• Computing stable eigendecompositions of matrix pencils
• The matrix equation \(X-AXB=C\) and an analogue of Roth's theorem
• Linear matrix equations: The module theoretic approach
• On matrix equivalence and matrix equations
• Roth's theorems and decomposition of modules
• Matrix equivalence and isomorphism of modules
• Eigenvalues and eigenvectors of symmetric centrosymmetric matrices
• Roth's theorems over commutative rings
• Roth's theorems for matrix equations with symmetry constraints
• The extension of Roth's theorem for matrix equations over a ring
• Explicit solution of the matrix equation \(AXB-CXD=E\)
• Roth's removal rule revisited
• The matrix equation \(AXB-GXB=E\) over the quaternion field
• Constant solutions of polynomial equations
• Centrosymmetric (Cross-Symmetric) Matrices, Their Basic Properties, Eigenvalues, and Eigenvectors
• Methods for the solution ofAXD−BXC=E and its application in the numerical solution of implicit ordinary differential equations
• Roth's Equivalence Problem in Unit Regular Rings
• Classroom Note:Centrosymmetric Matrices
• Consistency of a pair of generalized Sylvester equations
• Classroom Note: Some Eigenvalue Properties of Persymmetric Matrices
• The Equations AX - YB = C and AX - XB = C in Matrices

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