May 1 |
1.1, 1.2 |
Brief review of matrix arithmetic |

May 6 |
1.3, 1.4 |
Brief review of linear transformations, gaussian elimination, and elementary matrices |

May 8 |
1.5 |
Right, left, and two-sided matrix inverses |

May 13 |
1.5 |
Right, left, and two-sided matrix inverses |

May 15 |
1.6 |
LU factorization |

May 22 |
1.6, 2.1 |
LU factorization (cont.), ill-conditioned systems |

May 27 |
2.2, 2.3 |
Vector and matrix norms |

May 29 |
2.3, 2.4 |
Sensitivity and conditioning |

Jun 1 |
3.1, 3.2 |
Orthogonal complements, projections, Gram–Schmidt algorithm, diagonalization |

Jun 3 |
3.3 |
Hermitian and unitary matrices |

Jun 5 |
3.3, 3.4 |
Unitary diagonalization, Schur decomposition |

Jun 10 |
3.4 |
Spectral theorem, Cayley–Hamilton theorem |

Jun 12 |
3.5 |
Positive definite matrices, Cholesky factorization |

Jun 17 |
3.6 |
QR factorization |

Jun 19 |
1.1–3.5 |
**Midterm test** |

Jun 24 |
3.6, 3.7 |
QR factorization, computing eigenvalues |

Jun 26 |
3.7 |
Computing eigenvalues, Gershgorin circle theorem |

Jul 3 |
4.1 |
Singular value decomposition |

Jul 8 |
4.2, 4.3 |
Fundamental subspaces, principal components, pseudoinverses |

Jul 10 |
4.4, 4.4 |
Pseudoinverses, Jordan canonical form |

Jul 13 |
4.4, 4.5 |
Jordan canonical form, the matrix exponential |

Jul 15 |
5.1, 5.2 |
Quadratic forms and their diagonalization |

Jul 17 |
5.3 |
Rayleigh's principle, min-max theorem |

Jul 22 |
Notes |
Review |