Conclusion
Tensors in Data Sciences

The use of tensors in the world of engineering has undeniable advantages: certain problems had remained unsolvable without their help. This is particularly true of blind source separation, where the key property is the uniqueness of the CPD.

What happens when we go from the order D = 2 to the order D = 3? The matrix SVD M = UΣV^H can be seen both as a CPD where the matrix-factors U and V^* have orthogonal columns, or as an MLSVD where the core tensor Σ is diagonal. When we go from the order D = 2 to the order D = 3, we cannot preserve these two properties, as the tensor rank may exceed the dimensions. And why should it? Simply because the number of free parameters increases, as we have seen with the equation