I gained some great intuition from http://matrixmultiplication.xyz/ and (of all things) a paper named "An Introduction to Quantum Computing"[0].

Page 3 of that paper lays out matrix multiplication (e.g.: applying a "transformation matrix" in the spatial parlance of 3blue1brown's videos) as a traversal of a directed graph.

This isn't super readable (it's from my notes to self), but my intuition is:

Matrix multiplication is a graph traversal:

* Each i,j in transform matrix (on left) pulls N (the value at that index) times the j-th value in the input vec (on right) into the i-th output vec index

* This is equivalent to an N weighted vertex from the j-th node to i-th node, so i takes N of j's previous value

* The input (right side) is a matrix? It's just multiple column vectors next to each other, repeat the above process and make a new output vector for each iteration

[0]: https://arxiv.org/abs/0708.0261

> I gained some great intuition from http://matrixmultiplication.xyz/ and (of all things) a paper named "An Introduction to Quantum Computing"[0].

Just wanted to say thanks for this paper. It really does help with intuition and it's not something I would've expected to get through.

If you have gone through a first linear algebra course (e.g. watched Strang’s 18.06 videos), follow up with Strang’s videos for his class 18.065

https://www.youtube.com/watch?v=YiqIkSHSmyc&list=PLUl4u3cNGP...