The matrix equation \(XA-BX=R\) and its applications

DOI10.1016/0024-3795(88)90200-5zbMath0656.15006OpenAlexW2077639960MaRDI QIDQ1109847

Karabi Datta

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)90200-5

zbMATH Keywords

inertiacommuting matricesmatrix equationSylvester equationBézoutianssymmetrizerscommon eigenvalues

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Canonical forms, reductions, classification (15A21)

Related Items (12)

Perturbation theory and backward error for \(AX - XB = C\) ⋮ The matrix equation \(XA=A^ TX\) and an associated algorithm for solving the inertia and stability problems ⋮ Unique Full-Rank Solution of the Sylvester-Observer Equation and Its Application to State Estimation in Control Design ⋮ The linear bi-spatial tensor equation \(\varphi_{ij}A^iXB^j=C\) ⋮ Applications of linear transformations to matrix equations ⋮ Controllability and nonsingular solutions of Sylvester equations ⋮ Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation ⋮ New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian ⋮ Mixed, componentwise condition numbers and small sample statistical condition estimation of Sylvester equations ⋮ Parallel and large-scale matrix computations in control: Some ideas ⋮ The ubiquitous Kronecker product ⋮ Linear and numerical linear algebra in control theory: Some research problems

Cites Work

• Unnamed Item
• On eigenvalue and canonical form assignments
• On the similarity transformation between a matrix and its transpose
• Lyapunov, Bézout, and Hankel
• The Lyapunov matric equation SA+A*S=S*B*BS
• Controllability, Bezoutian and relative primeness
• Controllability, observability and the solution of AX-XB=C
• An algorithm for computing powers of a Hessenberg matrix and its applications
• Nonsingular solutions of TA-BT=C
• On the effective computation of the inertia of a non-hermitian matrix
• Inertia theorems for matrices: the semidefinite case
• The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations
• A Hessenberg-Schur method for the problem AX + XB= C
• Bezoutiants, Elimination and Localization
• Explicit Solutions of Linear Matrix Equations

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