English

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

Rings and Algebras 2019-05-10 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1810.05033,
  title  = {Lyapunov matrix equation $A^HX+XA+C=O_r$ with $A$ a Jordan matrix},
  author = {Dan Comănescu},
  journal= {arXiv preprint arXiv:1810.05033},
  year   = {2019}
}