Started reading The Manga Guide to Linear Algebra
The Manga Guide to Linear Algebra
Why?
Yes, this might sound weird if you don’t know the concept, but hear me out. After seing it praised on Twitter/X by an anon, I got myself a copy of The Manga Guide to Linear Algebra.
It’s pretty good if you want to quickly get up to speed, develop intuition, but does not go too deep into formal proofs.
You might not know me, but before going to a Software Engineering School, I studied math for 2 years in Uni, and dropped out because it was too “theorical”, not concrete enough for me, I needed to grok the formulas, to visualize, feel the proofs naturally and see the applications. Sadly, partly due to how Uni works — partly due to playing League of Legends too much — I did not get the level of understanding required for my attention to stick.
Now that I’ve become a SWE, I’ve seen the practical uses of such Math, and I now find myself needing more of it! So, step by step I’ll try to go from intuition and basics (this book) -> implementing existing algorithms -> proofs and more advanced formulas and theorem (some other textbook like Linear Algebra Done Right) -> understanding ML architecture choices -> being able to invent/discover new arch and techniques?
What I learned so far
Being somewhat familiar with Linear Algebra and computer science, I already knew a few things, so I read pretty fast through the first bits.
The first thing I learned were the techniques for computing the determinant for matrices of dimensions 4 and above. There’s a technique based on the generalisation of the formula \(\det(\mathbf{A}) = a_{11}a_{22} - a_{12}a_{21}\).
Along with the interpretation/intuition for the determinant (consolidated by 3b1b).
But there’s also an algorithm (LU decomposition) used in computer science based on a set of rules for determinant and gaussian reduction.