The matrix equation XA-AX=f(X)

Details The matrix equation XA-AX=f(X) The matrix equation XA-AX=f(X)

2010-05-18

arxiv.org/abs/1005.3159v1

Mathematics

Rings and Algebras

11 pages

Scientific paper

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.

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