Lecture Notes

Notes on fundamental topics in (applied) mathematics and machine learning.

Linear Algebra

  1. Vector Spaces
  2. Subspaces
  3. Basis and Dimension
  4. Linear Maps and Matrices
  5. Interpretations of Linear Maps
  6. Null Spaces and Ranges
  7. Inverses and Isomorphisms
  8. Column Rank Equals Row Rank
  9. Inner Products
  10. Isometries
  11. Eigenvectors and Diagonalization
  12. Symmetric Matrices
  13. Matrix Norms
  14. Ellipsoids
  15. Singular Value Decomposition
  16. QR Factorization
  17. Projections
  18. Least Squares
  19. Principal Component Analysis
  20. Loewner Order and Spectral Inequalities

Probability

  1. Functions of Random Variables

Optimization

  1. Rates of convergence