Quadratic forms on symmetry classes of tensors |
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Authors: | Herbert A. Robinson |
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Affiliation: | 1. University of California , Santa Barbara, California, 93106;2. National Bureau of Standards , Washington, D.C., 20234 |
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Abstract: | Let V:1,…,Vm be inner product spaces, and let L be a linear transformation on V1 ?…?Vm which satisfies (Lz,z)=0 for every decomposable tensor z. It is known that if the field is the complex numbers, then (Lz,z)=0 for every z. This paper contains a short proof of this result, an extension of it to arbitrary symmetry classes of tensors, and an analysis of its failure when the field is the real numbers. |
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Keywords: | AMS-MOS Subject Classification: 15A69. |
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