Linear Algebra — ZeroCourse

reading · we frame, you read MIT or the canonical taught · we author, no canonical fits ↺ spirals back to earlier lessons

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reading · 35 min + ~304 min canonical

Vectors, Matrices, and the Geometry of Data

You are beginning the math that powers machine learning, and here is the single most liberating fact to carry into it: linear algebra is the most visual branch of mathematics — ev…

primary 3Blue1Brown — Essence of Linear Algebra (YouTube)

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reading · 35 min + ~304 min canonical L1

Vector Spaces: Independence, Span, Basis, and Dimension

The previous lesson said data lives in a vector space; this lesson asks the natural next question — what is the structure of that space, and what does its structure tell you about…

primary 3Blue1Brown — Essence of Linear Algebra (YouTube)

after L1 locked

reading · 35 min + ~304 min canonical L1

Solving and Inverting: Linear Systems, Gaussian Elimination, and Determinants

At the computational heart of an enormous amount of science, engineering, and machine learning is one deceptively simple question: given a matrix A and a vector b, find the vector…

primary 3Blue1Brown — Essence of Linear Algebra (YouTube)

after L2 locked

reading · 35 min + ~304 min canonical L1

Eigenvalues, Eigenvectors, and Diagonalization: The Axes That Matter

Eigenvalues and eigenvectors have a reputation for being the intimidating, abstract peak of a linear algebra course — the formula Av = λv looks like a wall. But the idea is one of…

primary 3Blue1Brown — Essence of Linear Algebra (YouTube)

after L3 locked

reading · 35 min + ~304 min canonical L1

SVD and PCA: The Linear Algebra of Understanding Data

This is the lesson everything in the course has been building toward — where the abstract machinery (vectors, spaces, rank, eigenvalues) resolves into two of the most powerful and…

primary 3Blue1Brown — Essence of Linear Algebra (YouTube)

after L4 locked

exercise reading · 15 min L1

Exercises: Easy (Warm-up)

- [ ] Compute dot product, cross product of 3D vectors by hand — 5 exercises — MML Ch2 - [ ] Solve a 3x3 system of equations using Gaussian elimination — Row echelon form — MML Ch…

after L5 locked

exercise reading · 30 min L1

Exercises: Medium (Core)

- [ ] Find eigenvalues and eigenvectors of a 3x3 matrix — Characteristic polynomial — MML Ch4 - [ ] Implement PCA from scratch in Python — Center data, compute covariance, eigende…

after L6 locked

exercise reading · 45 min L1

Exercises: Hard (Stretch)

- [ ] Implement image compression using SVD in Python — Keep top-k singular values, compare quality vs compression - [ ] Prove that rank(A) = rank(A^T) = rank(A^T A) — Linear alge…

after L7 locked

exercise reading · 60 min L1

Mini-Project

- [ ] Build a face recognition system using PCA (Eigenfaces) in Python — Load face images, compute eigenfaces, project new faces, find nearest match using Euclidean distance in ei…

after L8 locked

L10

project reading · 480 min L1

Project: Linear Algebra Library in Python

Implement Vector and Matrix classes from scratch (no NumPy for the core). Support: addition, scalar multiplication, dot product, matrix multiplication, transpose, determinant, inv…

after L9 locked

L11

project reading · 300 min L1

Project: PCA Image Compressor

Implement PCA from scratch using your linear algebra library (or NumPy). Load images, reshape to data matrix, compute covariance, eigendecompose, project to top-k components, reco…

after L10 locked

L12

project reading · 600 min L1

Capstone: Neural Network Math from Scratch

- [ ] Milestone 1: Matrix operations — matmul, transpose, element-wise ops (linear algebra) - [ ] Milestone 2: Forward pass — layers, activations (ReLU, sigmoid, softmax) - [ ] Mi…

after L11 locked

L13

assessment reading · 63 min L1

Self-Assessment: Linear Algebra

- [ ] What is a vector space? What are the requirements for a set to be a vector space? - [ ] What are eigenvalues and eigenvectors? What do they tell you about a matrix? - [ ] Wh…

after L12 locked

13 lessons. Read in order; spiral back when you need to. By the end you'll have used the core ideas twice — once on the abstract, once on something you'll meet at work next week.