Session 2 - Linear Algebra II

Rank, eigenvectors, PCA, and the SVD: how many dimensions a data table really has, and what varies together.

Topics covered

• The determinant, the inverse, and rank
• Collinearity and rank-one structure
• Eigenvectors, eigenvalues, and diagonalisation
• Complex eigenvalues as rotation
• Symmetric matrices, covariance, and PCA
• The singular value decomposition and low-rank approximation

Materials

• 📊 Slides
• ✏️ Exercise sheet
• ✅ Solutions