  In this paper we classify the symbols of the linear differential operators of
order $k$, which act from the module $C^\infty(\xi)$ to the module
$C^\infty(\xi^t)$, where $\xi\colon E(\xi)\to M$ is vector bundle over the
smooth manifold $M$, bundle $\xi^t$ is either $\xi^*$ with fiber
$E^*:=\mathrm{Hom}(E,\mathbb{C})$ or $\xi^\flat$ with fiber
$E^\flat:=\mathrm{Hom}(E, \Lambda^n T^*)$ and $C^\infty(\xi)$,
$C^\infty(\xi^t)$ are the modules of their smooth sections. To find invariants
of the symbols we associate with every non-degenerated symbol the tuple of
linear operators acting on space $E$ and reduce our problem to the
classification of such tuples with respect to some orthogonal transformations.
Using the results of C. Procesi, we find generators for the field of rational
invariants of the symbols and in terms of these invariants provide a criterion
of equivalence of non-degenerated symbols.
