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Tensor Rank, Invariants, Inequalities, and Applications
2013
SIAM Journal on Matrix Analysis and Applications
Though algebraic geometry over C is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the n × n × n tensors of rank n over C, which has as a dense subset the orbit of a single tensor under a natural group action. We construct polynomial invariants under this group action whose nonvanishing distinguishes this orbit from points only in its closure. Together with an explicit subset of
doi:10.1137/120899066
fatcat:lhxqarjomzfx3hcbnhlpq4idlu