Linear Algebra (Spring 2010) (M-I-T)

• Lecture 1: The geometry of linear equations (M-I-T)
• Lecture 2: Elimination with matrices (M-I-T)
• Lecture 3: Multiplication and inverse matrices (M-I-T)
• Lecture 4: Factorization into A = LU (M-I-T)
• Lecture 5: Transposes, permutations, spaces R^n (M-I-T)
• Lecture 6: Column space and nullspace (M-I-T)
• Lecture 7: Solving Ax = 0: pivot variables, special solutions (M-I-T)
• Lecture 8: Solving Ax = b: row reduced form R (M-I-T)
• Lecture 9: Independence, basis, and dimension (M-I-T)
• Lecture 10: The four fundamental subspaces (M-I-T)
• Lecture 11: Matrix spaces; rank 1; small world graphs (M-I-T)
• Lecture 12: Graphs, networks, incidence matrices (M-I-T)
• Lecture 14: Orthogonal vectors and subspaces (M-I-T)
• Lecture 15: Projections onto subspaces (M-I-T)
• Lecture 16: Projection matrices and least squares (M-I-T)
• Lecture 17: Orthogonal matrices and Gram-Schmidt (M-I-T)
• Lecture 18: Properties of determinants (M-I-T)
• Lecture 19: Determinant formulas and cofactors (M-I-T)
• Lecture 20: Cramer's rule, inverse matrix, and volume (M-I-T)
• Lecture 21: Eigenvalues and eigenvectors (M-I-T)
• Lecture 22: Diagonalization and powers of A (M-I-T)
• Lecture 23: Differential equations and exp(At) (M-I-T)
• Lecture 24: Markov matrices; fourier series (M-I-T)
• Lecture 24b: Quiz 2 review (M-I-T)
• Lecture 25: Symmetric matrices and positive definiteness (M-I-T)