# Math 115B: General Course Outline

## Course Description

**115B. Linear Algebra. (4)** Lecture, three hours; discussion, one hour. Requisite: course 115A. Linear transformations, conjugate spaces, duality; theory of a single linear transformation, Jordan normal form; bilinear forms, quadratic forms; Euclidean and unitary spaces, symmetric skew and orthogonal linear transformations, polar decomposition. P/NP or letter grading.

## Textbook(s)

S. Friedberg, et al, *Linear Algebra*, 5th Ed., Pearson.

## Schedule of Lectures

Lecture | Section | Topics |
---|---|---|

1 |
. |
Review of Math 115A, Chapters I and II |

2 |
2.6 |
Dual Spaces (This section looks short but the concepts are new and thus will take two lectures to do well) |

3 |
2.6 |
Dual Spaces |

4 |
. |
Review Sections 5.1 and 5.2 from 115A |

5 |
5.4 |
Invariant Subspaces and the Cayley Hamilton Theorem |

6 |
5.4 |
Invariant Subspaces and the Cayley Hamilton Theorem |

7 |
5.4 |
Invariant Subspaces and the Cayley Hamilton Theorem |

8 |
. |
Review Sections 6.1 - 6.4 including more detail than was done in 115A |

9 |
. |
Review Sections 6.1 - 6.4 including more detail than was done in 115A |

10 |
6.5 |
Unitary and Orthogonal Operators and their matrices |

11 |
6.5 |
Unitary and Orthogonal Operators and their matrices |

12 |
6.5 |
Unitary and Orthogonal Operators and their matrices |

13 |
6.6 |
Orthogonal Projections and the Spectral Theorem |

14 |
6.6 |
Orthogonal Projections and the Spectral Theorem |

15 |
6.6 |
Orthogonal Projections and the Spectral Theorem |

16 |
. |
EXAM |

17 |
6.11 |
The Geometry of Orthogonal Operators |

18 |
6.11 |
The Geometry of Orthogonal Operators |

19 |
6.11 |
The Geometry of Orthogonal Operators |

20 |
7.1 |
Jordan Canonical Form I (This is a long and intricate presentation that takes time; do examples along the way!) |

21 |
7.1 |
Jordan canonical Form I |

22 |
7.1 |
Jordan canonical Form I |

23 |
7.3 |
The Minimal Polynomial (It might actually be better to do this section right after the Cayley Hamilton Theorem) |

24 |
7.3 |
The Minimal Polynomial |

25-29 |
. |
At the discretion of the teacher. |