tensors

To echo krastanov, it is the case that all tensors can be represented as multi-dimensional arrays, but not all multi-dimensional arrays are tensors.

I see a lot of answers describing what tensors are, but none really describe why they're important.

The material is great, though, including the coverage of tensors, which served me well the next year in General Relativity (Thorne's last time teaching it).

Is it true that tensors are multidimensional arrays if they come from the space R^{m1 x m2 x...

Maxwell-Faraday Equations, differential geometry and curvature tensors for general relativity, matrix mechanics and operators for quantum mechanics.

Especially if information geometry ever grows and data scientists start to actually have to use real tensors.

Also saw a demo on training 2-layer nets for GMM using tensors, and they learnt the weights rather fast.

They use tensors here to mean simply multidimensional array.

For tensors, the most basic tensor decomposition, where a tensor a_ijk is approximated by sum_l b_li * c_lj * d_lk.

In these cases, tensors yield guaranteed learning using embarassingly parallel algorithms, so faster convergence & can be run on Spark.

If you know the graphical birdtracks/Penrose diagram/Feynman diagram/String diagram notation, then tensors aren't hard at all.

So using tensors in deep learning shows promise, though the techniques are in their infancy.

It is true that it is a very common abuse of nomenclature to call all multidimensional arrays "tensors".

Einstein had his tensors right what he did not have correct was "2 + 2".

Once you get an intuitive grasp of bivectors, it's not hard to "see" tensors as a linear map of bivector into bivector.

I really dislike the "collection of numbers that transforms in this way" definition of vectors, tensors, etc.

Tensors can be somewhat intimidating, but it definitely would not take a year to understand tensors.

Tensors are most definitely not just multidimensional arrays.