Step 1
Vectors, Matrices, and Linear Maps
Know what the objects are and how a matrix acts on a vector.
Practice: Given a batch matrix, state what each axis means before multiplying.
Math Foundations
Master Linear Algebra
A focused route through the linear algebra that powers PCA, optimization, embeddings, attention, and neural networks.
Time
~14 hours
Core loop
object → shape → operation → geometric meaning → ML use
Topics
8 ordered topics
End state
You can read matrix-heavy ML pages without stopping at every symbol, and you know which algebraic object is doing the work.
Checkpoint 1
Vectors and Linear Maps
Treat vectors as objects and matrices as transformations, not just tables of numbers.
Open Vectors, Matrices, and Linear Maps
Step 2
Matrix Operations and Properties
Multiply, transpose, invert when valid, and check dimensions before computing.
Practice: Predict the output shape of three chained matrix products.
Checkpoint 2
Eigenvectors, SVD, and Geometry
Explain directions, variance, rank, projections, and low-dimensional structure.
Step 1
Matrix Norms
Measure vector and matrix size in ways that match ML stability arguments.
Practice: Compare Frobenius and spectral norm interpretations for a weight matrix.
Step 2
Eigenvalues and Eigenvectors
Identify invariant directions and why they matter for covariance and dynamics.
Practice: Explain what a dominant eigenvector says about repeated multiplication.
Step 3
Singular Value Decomposition
Decompose a matrix into rotations, scalings, and low-rank structure.
Practice: Use singular values to reason about rank and reconstruction error.
Step 4
Principal Component Analysis
See how covariance, eigenvectors, and projection become a learning method.
Practice: Describe why PCA keeps directions with high variance.
Checkpoint 3
Matrix Calculus for ML
Connect Jacobians, Hessians, and matrix derivatives to optimization and backprop.
Step 1
The Jacobian Matrix
Track how vector-valued functions change with respect to vector inputs.
Practice: State the Jacobian shape for a function from R^d to R^k.
Step 2
Matrix Calculus
Use gradients and matrix derivatives without losing shape discipline.
Practice: Derive the shape of a gradient before writing the formula.
How to use this path
Do not only read the pages. For each step, write the shape ledger, answer the practice prompt, and then run a small quiz or diagnostic. The goal is operational fluency: you should be able to predict what changes before code or algebra tells you.
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