Step 1
Linear Algebra
Vectors, matrices and transformations. Almost every calculation in machine learning, computer graphics and games is a matrix operation.
- Vectors and matrices
- Systems of linear equations
- Matrix multiplication and inverse
- Vector spaces and rank
- Determinants
- Eigenvalues and eigenvectors
- Least squares
Why it matters
An image is a matrix of pixels, a neural network layer is a matrix multiplication, and every rotation and scaling in a game is a transformation matrix. Even the coefficients of linear regression come from a matrix equation. Without this course you memorize machine learning formulas without understanding them.
What to know
- Vectors, the dot product, length and angle.
- Seeing matrix multiplication as a transformation: rotation, scaling, projection.
- Systems of linear equations and Gaussian elimination.
- Inverse, rank and vector spaces (column space, null space).
- Determinants and what they mean.
- Eigenvalues and eigenvectors; the basis of PCA.
- Least squares: the closest solution to a system with no exact solution (which is linear regression).
Practice and projects
- Watch 3Blue1Brown's "Essence of Linear Algebra" series before the course; it gives a visual picture of each topic.
- Try matrix operations with NumPy; load an image as a matrix and rotate and scale it.
- Solve linear regression yourself without a library, with the normal equation (XᵀX)⁻¹Xᵀy.
Common mistakes
- Learning only the calculations and skipping the geometric meaning.
- Assuming matrix multiplication is commutative (AB = BA).
- Solving equations in code by taking an inverse when numerically more stable methods (solve, lstsq) exist.