Lyapunov matrix equation A^HX+XA+C=O_r with A a Jordan matrix

2018/10/10 by Dan Comănescu, Comănescu, Dan
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1810.05033

openalex publication_date 2018/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Lyapunov matrix equation can be converted, by using the Jordan decomposition theorem for matrices, into an equivalent Lyapunov matrix equation where the matrix is a Jordan matrix. The Lyapunov matrix equation with Jordan matrix can be reduced to a system of Sylvester-Lyapunov type matrix equations. We completely solve the Sylvester-Lyapunov type matrix equations corresponding to the Jordan block matrices of the initial matrix.

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