The matrix equation \(X-AXB=C\) and an analogue of Roth's theorem

DOI10.1016/0024-3795(88)90204-2zbMath0656.15005OpenAlexW2061997834MaRDI QIDQ1109846

Harald K. Wimmer

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0024-3795(88)90204-2

zbMATH Keywords

Roth's theoremconsistency conditionmatrix equationmatrix pencil

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Matrix pencils (15A22)

Related Items (12)

On the solvability of generalized Sylvester operator equations ⋮ Operator substitution ⋮ Computational Methods for Linear Matrix Equations ⋮ The extension of Roth's theorem for matrix equations over a ring ⋮ Matrices over Quaternion Algebras ⋮ Simultaneous solutions of matrix equations and simultaneous equivalence of matrices ⋮ 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 \(q \mapsto \hat{q}\) ⋮ Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra ⋮ Restarted global FOM and GMRES algorithms for the Stein-like matrix equation \(X + \mathcal{M}(X) = C\) ⋮ Consistency of split quaternion matrix equations \(AX^{\star }-XB=CY+D\) and \(X-AX^\star B=CY+D\) ⋮ Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices ⋮ Coupled Sylvester-type Matrix Equations and Block Diagonalization

Cites Work

• On matrix equivalence and matrix equations
• Roth's theorems and decomposition of modules
• Roth's theorems over commutative rings
• Roth's removal rule revisited
• On the matrix equations $AX - XB = C$ and $AX - YB = C$
• The Equations AX - YB = C and AX - XB = C in Matrices

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