Linear Algebra Basics
Under the hood, ML and deep learning are linear algebra. Even a working intuition helps you understand what models do.
Learn it
Learn vectors and matrices, and the dot product. Build intuition (not heavy proofs): a matrix transforms data; a dot product measures similarity.
By the end you’ll be able to
- Work with vectors and matrices
- Understand dot products
Free resources
- 3Blue1Brown — Essence of Linear Algebra (playlist)(opens in a new tab)Start here
Visual, intuition-first vectors and matrices
Free~3 hr series - 3Blue1Brown — Vectors, what even are they? (Ch.1)(opens in a new tab)
Single-video starting point
Free10 min - Khan Academy — Linear Algebra(opens in a new tab)
Exercises on vectors and matrices
Freeself-paced
Practice
Compute a dot product of two vectors by hand and with NumPy; multiply two small matrices.
Build it — your output
A notebook that uses NumPy to do vector/matrix operations and explains in comments what each represents.
Prove it — check yourself
You’re ready to move on when you can honestly say yes to each:
- Can you compute a dot product?
- Do you know what a matrix does to a vector (intuitively)?
- Can you multiply matrices with NumPy?
Do it with AI
Use a free AI tool as your tutor and pair-programmer. Copy a prompt below into Claude, ChatGPT, or Gemini (for building, try Cursor or Copilot).
The habit: Try it yourself first — a little struggle is where the learning actually happens. Then ask for a hint before the answer — never copy blindly.
- Understand itClaude / ChatGPT / Gemini
I'm a beginner learning "Linear Algebra Basics". Explain it in simple terms with a real-world analogy, then ask me ONE question to check my understanding — don't reveal the answer.
- PracticeClaude / ChatGPT / Gemini
Give me 3 short practice problems on "Linear Algebra Basics" (my goal: work with vectors and matrices), from easy to hard. Don't include the solutions yet — I'll try them first, then ask you to check.
- Get unstuckClaude / ChatGPT / Gemini
I'm stuck on this exercise about "Linear Algebra Basics": [paste your attempt here]. Give me ONE small hint to move forward — do NOT give me the full solution.
- Build & reviewCursor / Copilot
Here is my work for a "Linear Algebra Basics" task: [paste your code or answer]. Review it: point out what's wrong and WHY, and suggest improvements — but let me make the fixes myself.
- Prove itClaude / ChatGPT / Gemini
Quiz me on "Linear Algebra Basics". Ask me 5 questions one at a time, wait for my answer each time, then tell me if I'm right and briefly why.