  We analyze the perturbation series for noncommutative eigenvalue problem
$AX=X\lambda$ where $\lambda$ is an element of a noncommutative ring, $ A$ is a
matrix and $X$ is a column vector with entries from this ring. As a corollary
we obtain a theorem about the structure of perturbation series for Tr $x^r$
where $x$ is a solution of noncommutative algebraic equation (for $r=1$ this
theorem was proved by Aschieri, Brace, Morariu, and Zumino, hep-th/0003228, and
used to study Born-Infeld lagrangian for the gauge group $U(1)^k$).
