> 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.
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