As someone who does teach tutorials as a side gig, I would argue that implementing matrix operations in a tutorial on neural networks is overkill. No matter what the level of the tutorial you always need to draw a line and assume a certain amount of background knowledge and knowing how to use standard tools isn't too much to ask. (yes, I know numpy isn't part of python's standard library, but it comes with pretty much any Python distribution as many other libraries depend on it.)

If we're talking about a longer format, such as a book, then we might consider digging deeper and implementing as much as possible using the barest of Python requirements. Indeed, Joel Grus does implement everything from scratch in his great (although a bit dated) book https://www.amazon.com/Data-Science-Scratch-Principles-Pytho....

EDIT: This is still a work in progress (and relies on numpy and matplotlib), but here is my version: https://github.com/DataForScience/DeepLearning These notebooks are meant as support for a webinar so they might not be the clearest as standalone, but you also have the slides there.

Matrix math is easy peasy. Freshman level programming. Just lookup algorithms on Wikipedia and you're all set.

The problem is it's extremely hard to make it efficient. Dozens of men-years are spent trying to optimize linear algebra libraries. There are handful linalg libraries that have competitive performance. It was my college project to make a fast linalg library, and boy it is fast. There are some things like matrix multiplication that if you implement in C with the trivial algorithm, takes >2 mins but with some tricks you can make it as fast as <second (vectorization, OpenMP, handwritten assembly, automatically optimized code, various optimizations, better algorithm.....).

So, if you want to implement linalg in some language and compile it, go ahead, more power to you. But it's basically impossible to do it efficiently. My opinion is: this is fine and we should do this. There should be linalg libraries written in pure python (and are 1000x slower than lapack) but just understand that it's impossible to satisfy all use cases of numpy this way (at least currently).

If you don't care much about performance (and if you are reimplementing a neural network from scratch you're probably doing it more as a learning project than anything else) implementing matrix operations isn't very difficult.

If you're not used to work with matrices simply reading the Wikipedia article might tell you enough to implement them yourself.

Exactly the reason why my colleagues and myself do all deep learning in C++, performance and portability, from cloud to RPie. We've even modified caffe2 so we could build the training graph from pure C++. We know this is not the current doxa :) It's also all open sourced just in case others might need it...

It is easy to do unless you don't code at all, or are completely confused by the math.

I'm a C# developer and I'm sure it would take me all of about 30 seconds to install a matrix multiplication package through nuget. I'm sure it would be immediately obvious how to add items to matrices or do a dot product.

Hm. I just finished teaching an ML course where all of the assignments were pure Python (on purpose, so students would actually have the chance to see all of the code). One of the assignments included implementing reverse-mode autodiff and a NN classifier on top. It can be done in ~600 lines of clear python, serious!

The complicated parts of Numpy are themselves a wrapper for the seminal LAPACK: http://www.netlib.org/lapack/. It has C language APIs, so that might help you with what you need to do.

Yep. I would like to see an article that implements everything without using matrices first, then creates the matrices library with you, and refactors everything over.

So much learning that we're missing by not going through this step.

I'm curious if you have a particular language/microcontroller/microwave/badger you have in mind? Depending on which, YMMV.