Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to solve the matrix equation XA-AX=f(X)   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.

27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci