Abstract
We suggest a different point of view on some aspects of classical invariant theory. A tensor is regarded as a multiply subscripted array of numbers which represents a multilinear form in a natural way. Two tensors are equivalent if they represent the same symmetric multilinear form. Canonical forms for symmetric 2×2×2 tensors are derived from this point of view and can be regarded as a generalization of Sylvester's law of inertia. In addition, some problems concerning the classification of cubic forms and cubic functionals under the action of various groups are suggested.
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