Introduction and Setup

This series is written to guide you through building your own linear algebra functionality from scratch.

Each section of the series focuses on a small, contained piece of functionality. By the end, you’ll have the foundation of a lightweight, modular linear algebra library that you can adapt for your own projects. You’ll also gain a better understanding of the mathematics behind it.

The examples are written in Rust, but the concepts are language-agnostic. If you’re comfortable in another language, you can follow along just as easily.

What You’ll Need

Before getting started, make sure you have the following:

  • A recent version of Rust installed
    You can check with:
    bash rustc --version If it’s not installed, visit https://rustup.rs to set it up.

  • A text editor or IDE that supports Rust
    VS Code with the rust-analyzer extension is a good option.

  • Basic familiarity with programming concepts and a little comfort with Rust syntax.
    You don’t need to be an expert — we’ll go step by step.

Project Setup

Create a new Rust project to follow along:

cargo new linear_algebra_from_scratch
cd linear_algebra_from_scratch

This will generate a new folder with a basic Cargo.toml and src/main.rs.

You can either implement everything directly in main.rs or create separate modules as the project grows.
For example:

src/
├── main.rs
└── math/
    ├── vec2.rs
    ├── vec3.rs
    └── matrix.rs

We’ll expand on this structure as we move through the guides.

How to Follow the Series

Each guide introduces one concept at a time: starting simple and building complexity gradually.
You’ll find three main sections in each:

  1. Concepts/Mathematical Background: an explanation of the underlying math and how it’s represented programmatically.
  2. Implementation: a series of tasks to write the code yourself.
  3. Solutions: a complete set of solutions showing one way to implement the concept.

You’re encouraged to write and test your own code before checking the solution.
There’s no single “right” way to implement these ideas, and exploring different approaches is part of the learning process.

Next Steps

When you’re ready, continue to the first real task: implementing a 2D vector type.
This will cover construction, basic arithmetic, and a few common operations used throughout linear algebra.

Continue to the next guide:
2D Vector Guide →

About the Author

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J. Cooper (JayCee) is a software developer, Maths enthusiast and musician based in the UK. They are the creator and maintainer of the lars crate and they have various other projects in progress

This article was published on October 29, 2025 with mkdocs.