The Matrix Equation $AX + XB = C$

DOI10.1137/0126003zbMath0245.15004OpenAlexW2070641733MaRDI QIDQ5656879

Vladimír Kučera

Publication date: 1974

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0126003

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Related Items (21)

The general nonstrict algebraic Riccati inequality ⋮ A general analysis of Sylvester's matrix equation ⋮ Pricing external barrier options in a regime-switching model ⋮ On solutions of generalized Sylvester equation in polynomial matrices ⋮ On the low-degree solution of the Sylvester matrix polynomial equation ⋮ On Lie and associative algebras containing inner derivations ⋮ Controllability, observability and the solution of AX-XB=C ⋮ The vectorial Ribaucour transformation for submanifolds of constant sectional curvature ⋮ Algebraic method for the study of some linear matrix equations ⋮ A thermodynamic basis for implicit rate-type constitutive relations describing the inelastic response of solids undergoing finite deformation ⋮ Symmetric, positive semidefinite, and positive definite real solutions of \(AX=XA^ T\) and \(AX=YB\) ⋮ A complete algebraic solvability test for the nonstrict Lyapunov inequality ⋮ 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 \(q \mapsto \hat{q}\) ⋮ Solution of the matrix eigenvalue problem \(VA+A^{*}V=\mu V\) with applications to the study of free linear dynamical systems ⋮ Some properties of solutions of Yule-Walker type equations ⋮ The group inverse of the nivellateur ⋮ Two-sided bounds on some output-related quantities in linear stochastically excited vibration systems with application of the differential calculus of norms ⋮ Block imbedding and interlacing results for normal matrices ⋮ Resolution of Conjectures Related to Lights Out! and Cartesian Products ⋮ The vec-permutation matrix, the vec operator and Kronecker products: a review ⋮ Factored forms for solutions of \(AX-XB=C\) and \(X-AXB=C\) in companion matrices

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