How to solve the matrix equation XA-AX=f(X)
Rings and Algebras
2012-07-03 v2
Abstract
Let f be an analytic function defined on a complex domain Omega and A be a (n,n) complex matrix. We assume that there exists a unique alpha satisfying f(alpha)=0. When f'(alpha)=0 and A is non derogatory, we solve completely the equation XA-AX=f(X). This generalizes Burde's results. When f'(alpha) is not zero, we give a method to solve completely the equation XA-AX=f(X): we reduce the problem to solve a sequence of Sylvester equations. Solutions of the equation f(XA-AX)=X are also given in particular cases.
Keywords
Cite
@article{arxiv.1005.3159,
title = {How to solve the matrix equation XA-AX=f(X)},
author = {Gerald Bourgeois},
journal= {arXiv preprint arXiv:1005.3159},
year = {2012}
}
Comments
12 pages. The title is changed. Published in Lin. Alg. and Appl