Linear Algebra MIT 18.06 (OCW)

Lectures by G. Strang, 2005

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List of Topics

  1. The Geometry of Linear Equations [1]
  2. Elimination with Matrices [2]
  3. Multiplication and Inverse Matrices [3]
  4. Factorization into $A = LU$ [4]
  5. Transposes, Permutations, Spaces $\mathbb R^n$ [5]
  6. Vector Subspaces: Column Space and Nullspace [6]
  7. Solving $A \mathbf x = \mathbf 0$: Pivot Variables, Special Solutions [7]
  8. Solving $A \mathbf x = \mathbf b$: Row Reduced Form $R$ [8]
  9. Independence, Basis, and Dimension [9]
  10. The Four Fundamental Subspaces [10]
  11. Matrix Spaces; Rank 1 Matrices; Small World Graphs [11]
  12. Graphs, Networks, Incidence Matrices [12]
  13. Quiz 1 Review [13]
  14. Orthogonality: Orthogonal Vectors and Orthogonal Subspaces [14]
  15. Projection onto Subspaces [15]
  16. Projection Matrices and Least Squares [16]
  17. Orthogonal Matrices and Gram-Schmidt [17]
  18. Properties of Determinants [18]
  19. Determinant Formulas and Cofactors [19]
  20. Cramer's Rule, Inverse Matrix, and Volume [20]
  21. Eigenvalues and Eigenvectors [21]
  22. Matrix Diagonalization and Powers of $A$ [22]
  23. Differential Equations and $\exp(At)$ [23]
  24. Markov Matrices; Fourier Series [24]
  25. Quiz 2 Review [25]
  26. Symmetric Matrices and Positive Definiteness [26]
  27. Complex Matrices; Fast Fourier Transform [27]
  28. Positive-Definite Matrices and Minima [28]
  29. Similar Matrices and Jordan Form [29]
  30. Singular Value Decomposition [30]
  31. Linear Transformations and Their Matrices [31]
  32. Change of Basis; Image Compression [32]
  33. Quiz 3 Review [33]
  34. General Inverses: Left and Right Inverses; Pseudoinverse [34]
  35. Final Course Review [35]


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