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

The number of independent invariants for m unit vectors and n symmetric second order tensors is 2m+ 6n-3