Gamas's theorem, in multilinear algebra, gives the necessary and sufficient conditions under which a tensor symmetrized by an irreducible representation of the symmetric group is forced to be zero. It was proved in 1988 by Carlos Gamas, with additional proofs later given by other mathematicians.
Facts
Statementthe above symmetrized tensor is non-zero if and only if it is possible to partition the set of vectors into linearly independent sets whose sizes are in bijection with the lengths of the columns of the partition 1 Classification
Statement FormCharacterization Theorem 1 Sources
1. Gamas's theorem - Wikipedia
Introduction
Gamas's theorem states that the above symmetrized tensor is non-zero if and only if it is possible to partition the set of vectors { v i } into linearly independent sets whose sizes are in bijection with the lengths of the columns of the partition ?.
References section
Carlos Gamas (1988). "Conditions for a symmetrized decomposable tensor to be zero." Linear Algebra and Its Applications.
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