Kruskal's theorem states that a sum of product tensors constitutes unique tensor rank decomposition if the so-called k-ranks are large. We prove "splitting theorem" for sets tensors, in which k-rank condition is weakened to standard notion rank, and conclusion uniqueness relaxed statement set splits (i.e. disconnected as matroid). Our splitting implies generalization theorem. While several exte...

We answer to a question posed recently in reference [Lovitz B, Petrov F. A generalization of Kruskal's theorem on tensor decomposition. Available at arXiv 2103.15633; 2021], proving the conjectured sufficient minimality and uniqueness condition 3-tensor

In this paper, we elaborate on a method to decompose multiloop multileg scattering amplitudes into Lorentz-invariant form factors, which exploits the simplifications that arise from considering four-dimensional external states. We propose simple and general approach applies both fermionic bosonic allows us identify minimal number of physically relevant can be related one-to-one independent heli...

Aslaksen, H., Determining summands in tensor products of Lie algebra representations, Journal of Pure and Applied Algebra 93 (1994) 135-146. We give some results that enable us to find certain summands in tensor products of Lie algebra representations. We concentrate on the splitting of tensor squares into their symmetric and antisymmetric parts. Our results are valid for any Lie algebra of arb...

We present an iterative algorithm, called the symmetric tensor eigen-rank-one iterative decomposition (STEROID), for decomposing a symmetric tensor into a real linear combination of symmetric rank-1 unit-norm outer factors using only eigendecompositions and least-squares fitting. Originally designed for quartic (4th-order) symmetric tensors, STEROID is shown to be applicable to any order throug...