Explicit solution of the matrix equation \(AXB-CXD=E\)

DOI10.1016/0024-3795(89)90708-8zbMath0682.15013OpenAlexW2095033200MaRDI QIDQ1824013

Maite Gassó, Vicente G. Hernández

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90708-8

zbMATH Keywords

Lyapunov equationCayley-Hamilton theoremmatrix equationSylvester equationmatrix pencilsingular pencils

Mathematics Subject Classification ID

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

Related Items (16)

On the Sylvester-like matrix equation \(AX+f(X)B=C\) ⋮ On solutions of the matrix equation \(AX=B\) with respect to semi-tensor product ⋮ The matrix equation \(AXB-GXB=E\) over the quaternion field ⋮ Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E ⋮ Dissipative performance control with output regulation for continuous-time descriptor systems ⋮ Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations ⋮ Contour integral solutions of Sylvester-type matrix equations ⋮ The solvability of two linear matrix equations ⋮ Updating \(\star \)-palindromic quadratic systems with no spill-over ⋮ Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra ⋮ On equivalence and explicit solutions of a class of matrix equations ⋮ Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm ⋮ Kronecker bases for linear matrix equations, with application to two-parameter eigenvalue problems ⋮ The solvability of linear matrix equations over a central simple algebra ⋮ Least squares pure imaginary solution and real solution of the quaternion matrix equation \(A X B + C X D = E\) with the least norm ⋮ Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)

Cites Work

• The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
• Lyapunov-like equations and reachability/observabiliy Gramians for descriptor systems
• Methods for the solution ofAXD−BXC=E and its application in the numerical solution of implicit ordinary differential equations
• The Matrix Equation $AXB + CXD = E$
• A Finite Series Solution of the Matrix Equation $AX - XB = C$
• Solution of the Equation $AX + XB = C$ by Inversion of an $M \times M$ or $N \times N$ Matrix
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Explicit solution of the matrix equation \(AXB-CXD=E\)