A matrix can do more than store data: it can transform it by stretching, rotating, and squashing space. Eigenvectors are the special directions that a transformation only stretches, and the eigenvalues tell you by how much. Finding them reveals the hidden structure inside a matrix.
The lessons start with eigenvalues and eigenvectors and why they matter in machine learning, then move to singular value decomposition (SVD), which breaks any matrix into simpler parts. They finish with PCA (principal component analysis), which uses these ideas to reduce many features to a few, and a NumPy walkthrough to put it all in code.
Watch the lessons in order, then continue on to Calculus Essentials.
An introduction to what eigenvalues and eigenvectors are, a good first stop before the machine learning applications.
Video 4minConnects eigenvectors and eigenvalues to PCA and shows why these ideas matter in machine learning.
Video 7minA visual explanation of singular value decomposition, showing what the factorization does to a matrix.
Video 16minAn overview of the SVD, a matrix factorization used throughout data science and machine learning.
Video 6minWalks through principal component analysis step by step with a complete worked example.
Video 30minA coding lesson that uses NumPy's linear algebra module for determinants, inverses, eigenvalues, SVD, and PCA.
Video 11min