Linear matrix equations: The module theoretic approach

DOI10.1016/0024-3795(89)90374-1zbMath0677.15001OpenAlexW2084886439MaRDI QIDQ1123234

Harald K. Wimmer

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)90374-1

zbMATH Keywords

characteristic polynomialslinear matrix equationsmodule structureLyapunov's equationroot location results for polynomials

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Other classes of modules and ideals in associative algebras (16D80)

Related Items (13)

On the Jordan form of a family of linear mappings ⋮ The group inverse of the transformation \(\mathcal{S}(X)=AX-XB\) ⋮ The matrix equation \(AXB-GXB=E\) over the quaternion field ⋮ The explicit solution of the matrix equation \(AX-XB = C\) ⋮ On the numerical analysis of generalized sylvester equations ⋮ On the numerical analtsys of generated sylvester equations ⋮ The quaternion matrix equation ΣA i XB i =E ⋮ Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra ⋮ Toward solution of matrix equation \(X=Af(X)B+C\) ⋮ A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity ⋮ The solvability of linear matrix equations over a central simple algebra ⋮ Generalized Lyapunov equations, matrices with displacement structure, and generalized Bézoutians ⋮ To solve matrix equation \(\sum A^iXB_i=C\) by the Smith normal form

Cites Work

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• Algebraic methods for Toeplitz-like matrices and operators
• Application of Hankel matrices of Markov parameters to the solutions of the Routh-Hurwitz and the Schur-Cohn problems
• Controllability, observability and the solution of AX-XB=C
• Algebraic method for the study of some linear matrix equations
• Inertia theorems for matrices, controllability, and linear vibrations
• Linear Matrix Equations Controllability and Observability, and the Rank of Solutions
• Formulae for the solution of Lyapunov matrix equations
• A Generalization of the Inertia Theorem
• On the Hermite-Fujiwara theorem in stability theory
• ALGEBRAIC CHARACTERIZATION OF POLYNOMIALS WHOSE ZEROS LIE IN CERTAIN ALGEBRAIC DOMAINS

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