Professional paper

Sylvester and Lyapunov matrix equations

Maja Kovačević ; Osnovna škola Jagode Truhelke, Osijek
Ivana Kuzmanović Ivičić ; Fakultet primijenjene matematike i informatike, Sveučilište J. J. Strossmayera u Osijeku

Abstract

Linear matrix equations are linear equations in which the unknown is a matrix. Due to their wide range of applications, the Sylvester equation stands out as one of the most important types of matrix equations, along with its special case – the Lyapunov equation. This paper presents the necessary and sufficient conditions for the existence and uniqueness of solutions of the Sylvester and Lyapunov equations, as well as their generalizations. Additionally, a description of the fundamental numerical algorithms used to solve these equations is provided.

Keywords

matrix equations, Sylvester equation, Lyapunov equation

Hrčak ID:

340525

URI

https://hrcak.srce.hr/340525

Publication date:

1.6.2025.

Article data in other languages: croatian

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