IlyaKisil

Was just explaining the meaning of “higher-order” within the context of this library. But thanks, now I have a clearer picture of what to include in the main README file and notebooks with tutorials, so to avoid misleading.

I would suggest to search on YouTube for Tamara Kolda: Tensor decompositions. She also published a very good introductory paper “Tensor decompositions and applications” in 2008.

I do agree that tensors are much more then just an array of data with N-indices and that numerical methods are oftentime forget about that.

Basically, order of a tensor is the number of dimensions of an array of data. Vector - one dimensional array or a tensor of order 1 Matrix - two dimensional array of data or a tensor of order 2 Three and more dimensional arrays of data are tensors of higher order.

Sorry for misleading. I am aware that the term "tensor" was originally introduced within physics. But then it was adopted in chemometrics, signal processing and machine learning in a context of N-dimensional arrays of data. As such, this toolbox is focused on multi-way analysis and tensor decompositions of N-dimensional data arrays (tensors). However, fundamental operations include folding/unfolding of the data, tensor-matrix product and contration with a vector or another tensor. The latter is not implemented at the moment, but will be in future releases. Not sure whether these opertations carry the same meaning as in physics though.