Ashutosh Patidar · notes

Linear Algebra (source: Gilbert Strang notes)

Lecture-by-lecture notes on MIT 18.06 Linear Algebra (Spring 2010, Prof. Gilbert Strang), read through an ML / DL / AI lens. The series opens with PCA from the IIT Madras MLT course, works through all 34 lectures in order, and closes with a condensed revision sheet.

How to read: pages go in the order we covered them. Side questions appear at the end of the lecture where they came up. Source: MIT OCW 18.06, Spring 2010.

  1. 00Prologue: Data Compression, PCA & Residue Analysis (IITM MLT L5)
  2. 01Lecture 1: The Geometry of Linear Equations
  3. 02Lecture 2: Elimination with Matrices
  4. 03Lecture 3: Multiplication and Inverse Matrices
  5. 04Lecture 4: Factorization into \(A = LU\)
  6. 05Lecture 5: Transposes, Permutations, Vector Spaces \(\mathbb{R}^n\)
  7. 06Lecture 6: Column Space and Nullspace
  8. 07Lecture 7: Solving \(Ax = 0\): Pivot Variables, Special Solutions
  9. 08Lecture 8: Solving \(Ax = b\): Row Reduced Form \(R\)
  10. 09Lecture 9: Independence, Basis, and Dimension
  11. 10Lecture 10: The Four Fundamental Subspaces
  12. 11Lecture 11: Matrix Spaces; Rank 1; Small World Graphs
  13. 12Lecture 12: Graphs, Networks, Incidence Matrices
  14. 13Lecture 13: Quiz 1 Review
  15. 14Lecture 14: Orthogonal Vectors and Subspaces
  16. 15Lecture 15: Projections onto Subspaces
  17. 16Lecture 16: Projection Matrices and Least Squares
  18. 17Lecture 17: Orthogonal Matrices and Gram–Schmidt
  19. 18Lecture 18: Properties of Determinants
  20. 19Lecture 19: Determinant Formulas and Cofactors
  21. 20Lecture 20: Cramer's Rule, Inverse Matrix, and Volume
  22. 21Lecture 21: Eigenvalues and Eigenvectors
  23. 22Lecture 22: Diagonalization and Powers of \(A\)
  24. 23Lecture 23: Differential Equations and \(e^{At}\)
  25. 24Lecture 24: Markov Matrices; Fourier Series
  26. 25Lecture 24b: Quiz 2 Review
  27. 26Lecture 25: Symmetric Matrices and Positive Definiteness
  28. 27Lecture 26: Complex Matrices; Fast Fourier Transform
  29. 28Lecture 27: Positive Definite Matrices and Minima
  30. 29Lecture 28: Similar Matrices and Jordan Form
  31. 30Lecture 29: Singular Value Decomposition
  32. 31Lecture 30: Linear Transformations and Their Matrices
  33. 32Lecture 31: Change of Basis; Image Compression
  34. 33Lecture 32: Quiz 3 Review
  35. 34Lecture 33: Left and Right Inverses; Pseudoinverse
  36. 35Lecture 34: Final Course Review
  37. 36Revision Notes & Formula Sheet (all 34 lectures, ML lens)