MIT 18.06, Linear Algebra, Spring 2005
prof. Gilbert Strang
  • Lecture 1: The Geometry of Linear Equations
  • Lecture 2: Elimination with Matrices
  • Lecture 3: Multiplication and Inverse Matrices
  • Lecture 4: Factorization into A = LU
  • Lecture 5: Transposes, Permutations, Spaces R^n
  • Lecture 6: Column Space and Nullspace
  • Lecture 7: Solving Ax = 0: Pivot Variables, Special Solutions
  • Lecture 8: Solving Ax = b: Row Reduced Form R
  • Lecture 9: Independence, Basis, and Dimension
  • Lecture 10: The Four Fundamental Subspaces
  • Lecture 11: Matrix Spaces; Rank 1; Small World Graphs
  • Lecture 12: Graphs, Networks, Incidence Matrices
  • Lecture 13: Quiz 1 Review
  • Lecture 14: Orthogonal Vectors and Subspaces
  • Lecture 15: Projections onto Subspaces
  • Lecture 16: Projection Matrices and Least Squares
  • Lecture 17: Orthogonal Matrices and Gram-Schmidt
  • Lecture 18: Properties of Determinants
  • Lecture 19: Determinant Formulas and Cofactors
  • Lecture 20: Cramer's Rule, Inverse Matrix, and Volume
  • Lecture 21: Eigenvalues and Eigenvectors
  • Lecture 22: Diagonalization and Powers of A
  • Lecture 23: Differential Equations and exp(At)
  • Lecture 24: Markov Matrices; Fourier Series
  • Lecture 25: Symmetric Matrices and Positive Definiteness
  • Lecture 26: Complex Matrices; Fast Fourier Transform
  • Lecture 27: Positive Definite Matrices and Minima
  • Lecture 28: Similar Matrices and Jordan Form
  • Lecture 29: Singular Value Decomposition
  • Lecture 30: Linear Transformations and Their Matrices
  • Lecture 31: Change of Basis; Image Compression
  • Lecture 32: Quiz 3 Review
  • Lecture 33: Left and Right Inverses; Pseudoinverse
  • Lecture 34: Final Course Review