Explicit Solutions of the Matrix Equation $\sum {A^i XD_i } = C$

DOI10.1137/0613067zbMath0765.15003OpenAlexW2001801344MaRDI QIDQ4021610

Harald K. Wimmer

Publication date: 16 January 1993

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0613067

zbMATH Keywords

Sylvester equationpolynomial matrixrealizationlinear matrix equationsimultaneous triangular formmodules over polynomial ringspairwise commutative matrices

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Matrices over function rings in one or more variables (15A54)

Related Items (8)

Operator substitution ⋮ Computational Methods for Linear Matrix Equations ⋮ The matrix equation \(AXB-GXB=E\) over the quaternion field ⋮ On solutions of generalized Sylvester equation in polynomial matrices ⋮ The quaternion matrix equation ΣA i XB i =E ⋮ Extension of Henrici's method to matrix sequences ⋮ The solvability of linear matrix equations over a central simple algebra ⋮ To solve matrix equation \(\sum A^iXB_i=C\) by the Smith normal form

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