  Anisotropic invariants play an important role in continuum mechanics. Knowing
the number of independent invariants is crucial in modelling and in a rigorous
construction of a constitutive equation for a particular material, where it is
determined by doing tests that hold all, except one, of the independent
invariants constant so that the dependence in the one invariant can be
identified. Hence, the aim of this paper is to prove that the number of
independent invariants for a set of $n$ symmetric tensors and $m$ unit vectors
is at most 2m+ 6n-3. We also give relations between classical invariants in the
corresponding minimal integrity basis.
