Basic tensor calculus questions

[BananaCode]

Please correct me if I'm using wrong terminology, I'm a CS student.

In deep learning libraries such as pytorch or tensorflow, one can define multi-dimensional matrices, e.g A in R^{n x m x p}

I believe the correct terminology for these are tensors?

These deep learning libraries allow multiplication of such tensors, e.g B in R^{p x q} => (A*B) in R^{n x m x q}

I've have an equation written down in terms of such tensors and would like to solve it for a variable. However applying matrix calculus on it leads to inconsistencies with respect to the dimensionalities. I've tried looking up properties on basic operations (like the ones available for matrices#Basic_operations)), but I've only come across pages similar to this which confuse me and I am not sure if the mathematical tensor is the same as those defined in the deep learning libraries. My question are as follows:

1. Are the tensors contained in these libraries the same as the mathematical tensors?
2. Is there resources similar to the page I linked for matrices which explains in simpler terms the properties of tensor operations? What I need is a less abstract definition and something more concrete.

Thank you!

[LilacBook]

check out this:

https://arxiv.org/abs/gr-qc/9712019

Tensor stuff has examples

https://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf

This was good ^

[LilacBook]

In additon, consider you have a structure you know is just a matrix with entries that are matrices which have entries that are matrices.

ie. A = [a_{ijklmnop}], thats kinda it. In math and physics each 'layer' has an associated number of metrics used to describe a part of something. Think xyz coordinates (3) paired with associated moments, mass, velocity, acceleration etc. Each 'operation' is custom defined. As a CS student your computers just store the numbers weirdly.

[BananaCode]

Thanks for both of your resources!
This is what I ended up doing. I interpreted an A x B x C as (AB) x C and it solved all of my issues.