# To what extent does machine learning make use of tensor algebra/calculus? [duplicate]

Is it useful to know something about tensor algebra or tensor calculus if one is interested in deeplearning?

My question relates to both ML practice, and ML theory (but perhaps more to ML theory).

EDIT: the existence of n-index arrays in ML is what motivates my question, but I am asking about the tools of tensor algebra/calculus. (Tensors can be represented by n index arrays, but the analysis is more abstract).

• Are you referring to higher-dimensional tensors or just matrices and linear applications? – David Jun 26 '19 at 10:21
• @David. I am talking about that which one would learn in a tensor algebra/tensor calculus class, which isn't also in a linear algebra class. So probably higher dimensional tensors. I think for example in the context of convolutional networks this seems to be relevant? – user56834 Jun 26 '19 at 10:34
• So you are probably refering to "$n$-index arrays" with $n>2$, am I right? – David Jun 26 '19 at 10:37
• @David, the existence of n-index arrays in ML is what motivates my question, but I am asking about the tools of tensor algebra/calculus. (Tensors can be represented by n index arrays, but the analysis is more abstract). – user56834 Jun 26 '19 at 11:12
• I marked it as a duplicate of another thread (pretty detailed!). The questions differ, but they seem to ask about the same thing. If you find that the other thread does not answer your question, please comment, we may re-open it. – Tim Jun 26 '19 at 11:23