I’ve been working on linear algebra in APL and I decided to write an article on one of the fundamental operations of linear algebra (and neural networks), matrix multiplication! In this post I walk through how to multiply a 2x2 array by a 2x1 array.

And there’s no matrix multiplication glyph !

This post walks through:

What is matrix multiplication and manual calculation in this simple example

How to do matrix multiplication in APL step by step and how and why it works (including explaining the dot glyph)

Shows a first (relatively) simple example of how glyphs will combine in a really powerful and flexible ways. Matrix multiplication for example is +.x, rather than having a glyph specific to matrix multiplication.

Hey all - I got a question about how this works with a matrix times a matrix instead of a matrix times a vector, so I updated the post to include an example showing that it works the same way with 2 matrices!