On increase at infinity of almost hypoelliptic polynomials

It is proved that an almost hypoelliptic polynomial $P(\xi)=P(\xi_1,\dots,\xi_n)$ is increasing at infinity, i. e. $|P(\xi)|\to\infty$ as $|\xi|\to\infty$, if and only if the number $n$ of variables of $P$ is invariant with respect to any linear nondegenerate transformation $T\colon R^n\to R^n$.