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In Matlab Tensor Toolbox there is a tensor type called "Kruskal tensors", I found its form is similar to the CP decomposition.

Wikipedia mentioned:

"As such, many of the methods have been independently invented several times, often with subtle variations, leading to a confusing literature. Abstract and general mathematical theorems are rare (though see Kruskal[1] with regard to the CP decomposition)"

In a paper on [A concise proof of Kruskal's theorem on tensor decomposition], it mentioned:

"...In these fields, the expression of a tensor as a sum of rank-1 tensors is often referred to as the Candecomp or Parafac decomposition."

So, what is the relation or difference between Kruskal tensor decomposition and CP decomposition?

Are they actually the same thing but Kruskal decomposition is devised by a different person in different field for third-order tensor?

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