Canonical forms for symmetric tensors

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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.

Original languageEnglish
Pages (from-to)271-282
Number of pages12
JournalLinear Algebra and Its Applications
Volume57
Issue numberC
DOIs
StatePublished - Feb 1984

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