Linear Algebra: The Math of What Happens If I Change This?
If you have ever moved a character in a 2D game, applied a filter to a photo, or watched a recommendation system suggest something you might like, you have used linear algebra. The difference is that the computer knew it was doing linear algebra, and you did not.
This guide fixes that. We are not going to drill matrix multiplication until your eyes bleed. We are going to start from something you already understand - walking in a direction - and build up to the notation and the ideas. By the end, a matrix will look like a recipe card: "rotate everything 90 degrees" or "make everything twice as big." That is all it is.
This is the sixth guide in the Mathematics track. It assumes nothing beyond the mindset and notation from Why Math Is Not Your Enemy and the set idea from Sets, Relations, and Functions. If you can read a sentence and follow a recipe, you can do this.
How to read this
- Here for the "what is this even for" answer? Start with Phase 1 - vectors as real movements.
- Want the whole toolkit? Read in order - matrices build on vectors, and the applications build on both.
The phases
- Vectors as Arrows in the Real World - direction and magnitude, adding movements, and the code that moves a character.
- Matrices as Recipes for Transformation - scaling, rotating, and shearing, and what matrix multiplication actually does to a shape.
- Why This Is Everywhere - PageRank, recommendation systems, neural networks, and the builder's guide to seeing linear algebra in the wild.
This builds on Numbers & Number Systems (coordinates as numbers) and pairs with Counting & Combinatorics (dimensions as choices). It sets up the machinery behind much of modern computing.