Solution of the Matrix Equations $AX + XB = - Q$ and $S^T X + XS = - Q$

DOI10.1137/0118061zbMath0205.05102OpenAlexW2139029562MaRDI QIDQ5604565

Peter C. Müller

Publication date: 1970

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

Full work available at URL: https://doi.org/10.1137/0118061

Mathematics Subject Classification ID

Matrix equations and identities (15A24)

Related Items (14)

Principal axis intrinsic method and the high dimensional tensor equation \(AX-XA=C^*\) ⋮ The linear bi-spatial tensor equation \(\varphi_{ij}A^iXB^j=C\) ⋮ New expressions for the solution of the matrix equation \({\mathbf A}^ T{\mathbf X}+{\mathbf X}{\mathbf A}={\mathbf H}\) ⋮ The inversion-free iterative methods for a system of nonlinear matrix equations ⋮ Resultants and Lyapunov matrix equations ⋮ Twirl tensors and the tensor equation \(AX-XA=C\) ⋮ The solution of the matrix equation XC – BX = D as an eigenvalue problem ⋮ Vector structures and solutions of linear matrix equations ⋮ Explicit solutions of the matrix equation AX - XB = C ⋮ The tensor equation \(AX +XA = \Phi (A,H)\), with applications to kinematics of continua ⋮ Approximations and error bounds for computing the inverse mapping ⋮ The inversion-free iterative methods for solving the nonlinear matrix equation \(X + A^H X^{- 1} A + B^H X^{- 1} B = I\) ⋮ On the derivative of the square root of a tensor and Guo's rate theorems ⋮ Generalized Lyapunov equations, matrices with displacement structure, and generalized Bézoutians

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