The plan
This page is a sequence, not a pile of links. Each stage says what to do, how long it takes, and how you will know you are done. If you only remember one thing: solving beats watching, every single week.
How you study matters more than what you study. Every lecture here is built for the same five-step loop. It takes discipline for a week. Then it becomes a habit.
Flip through the slides once, fast. Two minutes. You are not learning yet. You are building a map so nothing later surprises you.
Read slowly. At each diagram, close it and draw it from memory, labels too. If you can't, read that part again. The drawing is the test.
Before you run each code block, say what it will print. Then change the numbers until something breaks, and look at what broke.
Do the exercises. Then a few MIT problems. Watch Strang only after you have solved. It lands better when you struggled first.
Explain the idea in five sentences to a friend. Tomorrow, derive the formula again. Next week, one more problem. That is what makes it permanent.
One warning. Watching lectures feels productive long before it is. Here, video comes after solving, as the reward for it.
One hour a day, at the Stage 2 pace of two lectures a week. The schedule matters more than the hours.
Before you start
You need school algebra, the idea of a function, and enough Python to run a script. That is all. You do not need calculus. When a lecture wants an idea from calculus, it builds that idea on the spot.
If solving 2x + 3 = 7 feels rusty, spend a weekend here first. Nothing else is missing.
Done when: You can plot the point (2, 3) and solve 2x + 3 = 7 without thinking.
Week 1. About 4 hours
Watch Essence of Linear Algebra from start to finish before you study anything. No notes. No pausing to memorize. Let the animations put the core pictures in your head: vectors are arrows, matrices move space, determinants scale volume. Everything in this course hangs on those pictures.
Sixteen short chapters. The most useful four hours in math education.
Done when: You can explain to a friend, waving your hands, what a matrix does to space.
Months 1 to 3. About 80 hours
Work through the lectures here in order, with the five-step method. One lecture every two or three days is a good pace. Speed is not the goal. Each lecture page names its matching Strang video and book sections, so pair them as you go.
You are here. Begin at Lecture 0.
The classic lectures. Watch after solving, not before.
The same course rebuilt for self-study. Recitation videos and worked exams for every unit.
The book both courses follow. Some sections are free on its site.
The live MIT semester. Notes, problem sets, Julia notebooks.
Done when: You can find a null space by hand, draw the four fundamental subspaces on a blank page, and say what least squares minimizes.
Every week, from week 2. About 30 hours
Reading feels like understanding. Solving is understanding. Do problems from the first week on, and treat every wrong answer as the system working. At the end of each part of the course, sit a real MIT exam with the clock running and the book closed.
Real exams from 1997 to 2015, with solutions.
Array drills with solutions, easy to devious.
Coding problems for ML math, graded online.
Done when: You pass an archived Exam 1 with the book closed and the clock running.
Months 3 to 5. About 40 hours
This is where the course pays off: the SVD, low-rank structure, PCA, and the linear algebra inside neural networks. Read Strang's data book next to Part VI of this course. Most of all, build things.
The bridge book. SVD, optimization, neural networks.
Strang's follow-up course for the machine learning era, fully filmed.
Free book. Connects linear algebra to regression, PCA, and SVMs.
Every derivative used in deep learning, derived slowly.
The same decompositions at real scale, in Python.
Done when: You can write PCA in plain NumPy and defend every line.
Whenever you want more
Linear algebra rewards a second pass at a higher level. Axler rebuilds the subject through proofs. Trefethen and Bau rebuild it through computation. Pick the one that matches where you are going, or take both.
The standard rigorous text. Free from the author, with his lecture videos on the same page.
Full university courses on abstract linear algebra, following Axler.
How the algorithms behave in floating point. The standard numerical text.
A gentler formal book with very good exercises. Free, with Julia and Python companions.
Done when: You read a proof of the spectral theorem for fun.
In this order. Most confusion dies at step one.
Draw the 2 by 2 case by hand. Most confusion cannot survive a small example. If it does, you found the real question.
Check it in NumPy. Ten seconds, no judgment. The computer settles arguments you are having with yourself.
Watch the matching recitation on 18.06SC. A different teacher, working a full problem. That is what recitations are for.
Read the same idea in Interactive Linear Algebra. A second telling with live figures. Often the second telling is the one that lands.
Ask on Math Stack Exchange. Show what you tried. Half the time you find the answer while writing the question.
Almost everyone who abandons this subject does it one of these ways. Name them and they lose most of their power.
Watching without solving. It feels like progress. It is not.
Memorizing steps instead of pictures. Steps decay in a week. Pictures last for years.
Skipping exercises because the reading made sense. Understanding you cannot use is not understanding yet.
Sprinting. Two lectures a day for a week, then nothing for a month. One hour a day beats both.
Nothing proves understanding like implementation. When the course introduces an algorithm, write it before you call the library. The classic ladder: matrix multiplication, then LU, then QR, then eigenvalues by power iteration, then a small SVD. These sites turn the ladder into graded practice, in order, from NumPy to GPU kernels.
Graded Python problems for ML math: matmul, power iteration, PCA. Start here.
A thousand algorithms from scratch, with the math and papers behind each. Runs in the browser.
Rebuild 21 tensor operations from one primitive. Pure array thinking.
Backpropagation in about a hundred lines. Then write your own without looking.
Write the derivative of each operation yourself. The best prep for backpropagation.
Build a small PyTorch clone as a structured course: tensors, broadcasting, autograd.
One level down. Write the GPU kernels for your matrix operations yourself.
CUDA challenges judged in the browser, on real GPUs. No setup, no cloud bill.
The same puzzle style for Triton, the language most new ML kernels are written in.
A good final project: eigenfaces. Load a face dataset, center it, compute the covariance, find the principal components with your own power iteration, and rebuild faces from twenty numbers. It uses everything in this course and fits in an afternoon.
Everything named here, plus the rest of the shelf, is in the library.