Linear Algebra
Vectors, matrices, eigenvalues, and the geometry behind machine learning.
- 01 Vectors and Vector Spaces: The Language of DataA first-principles guide to vectors, vector spaces, and their geometric meaning — the foundation of all machine learning mathematics.
- 02 Matrices and Matrix Operations: Organizing Linear ComputationMaster matrix arithmetic, special matrix types, and the rules of matrix algebra that power every ML algorithm.
- 03 Systems of Linear Equations: From Geometry to AlgorithmsSolve linear systems with Gaussian elimination, understand solution geometry through row echelon form, and connect to ML applications.
- 04 Determinants: The Volume Factor of Linear MapsUnderstand determinants as volume scaling factors, learn computation methods, and see how they reveal matrix invertibility.
- 05 Linear Transformations: Matrices as FunctionsSee matrices as geometric transformations — rotations, reflections, projections, and shears — and understand the connection to neural networks.
- 06 Inner Products, Norms, and Orthogonality: Measuring GeometryMaster inner products, distance metrics, orthogonal projections, and Gram-Schmidt — the geometric tools behind PCA, least squares, and embeddings.
- 07 Eigenvalues and Eigenvectors: The DNA of a MatrixDiscover eigenvalues and eigenvectors — the special directions that reveal a matrix's intrinsic behavior, powering PCA, PageRank, and spectral methods.
- 08 Matrix Decompositions: Breaking Matrices into Simpler PiecesMaster SVD, LU, QR, Cholesky, and eigendecomposition — the factorizations that power dimensionality reduction, compression, and numerical algorithms.
- 09 Linear Algebra in Machine Learning: Putting It All TogetherSee how vectors, matrices, eigenvalues, and decompositions drive real ML algorithms — from linear regression to Transformers and beyond.
- 10 Matrix Calculus: Derivatives for Machine LearningMaster gradients, Jacobians, Hessians, and the chain rule for vectors and matrices — the math that makes backpropagation work.
- 11 Tensor Operations: Beyond MatricesUnderstand tensors as multi-dimensional arrays, master Einstein notation and contractions, and see how PyTorch and TensorFlow think in tensors.
- 12 Sparse Matrices and Efficient ComputationLearn how sparse matrices save memory and speed up computation in NLP, graphs, and recommender systems — from storage formats to sparse solvers.
- 13 Randomized Linear Algebra: Speed Through RandomnessLearn how random projections, randomized SVD, and sketching algorithms solve massive linear algebra problems faster than classical methods.