Spring Term 2014

Lior Silberman
- Office: MATX 1112, 604-827-3031
- Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
- Office hours (Winter 2024): by appointment or
Time Location Zoom Meeting ID Zoom Password T 9:30-10:00 ORCH 3009 N/A N/A Th 9:30-11:00 ORCH 3009 and on Zoom 694 6667 3745 914585 F 11:45-13:00 at PIMS and on Zoom 676 1308 4912 139267

- Classes: MWF, 11:00-12:00, Georgraphy 200.
- Syllabus
- (Rough) lecture notes (updated 12/4/2014)

This is a second course in linear algebra, intended for honours students. There is no required textbook. The book by Halmos is very good, covers nearly everything, and is available in PDF form from the publisher for anyone on the UBC network; a lot of the material can also be found in any "abstract algebra" textbook. More details may be found in the syllabus.

- Halmos, Finite-dimensional Vector Spaces, available from SpringerLink
- Coleman, Calculus on Normed Vector Spaces, Chapter 1 (on SpringerLink)
- Higham, Functions of Matrices, available from SIAM
- [Your favorite author], Abstract Algebra

- Solutions (only) are stored on a secure website; registered students can
access them after first
**logging on to Connect**. - Problem set grade statistics.

- Problem Set 1, due 15/1/2014. Solutions.
- Problem Set 2, due 22/1/2014 (also as: LyX, LaTeX). Solutions.
- Problem Set 3, due 29/1/2014 [practice problems replaced] (also as: LyX, LaTeX). Solutions.
- Problem Set 4, due 7/2/2014. Solutions.
- Problem Set 5, due 14/2/2014 [problem 2 shortened; minor fixes in problems 1,4]. Solutions.
- Problem Set 6, due 28/2/2014. Solutions.
- Problem Set 7, due 10/3/2014 [problem 4 corrected]. Solutions.
- Problem Set 8,
**now due 19/3/2014**[calculational problem added]. Solutions. - Problem Set 9, due 26/3/2014. Solutions.
- Problem Set 10, due 7/4/2014 [problems 4(b),4(c), 6(a) corrected]. Solutions.

Section numbers marked § are in Halmos [1], section numbers marked N are in the course notes above.

Week | Date | Material | Reading | Notes |
---|---|---|---|---|

1 | M 6/1 | Introduction | §1,§2 | |

W 8/1 | Direct sum and product | §19,§20 | Note on infinite dimensions | |

F 10/1 | (continued) | |||

2 | M 13/1 | (continued) | ||

W 15/1 | Quotients | §21,§22 | PS1 due | |

F 17/1 | Duality | §13,§15 | ||

3 | M 20/1 | (continued) | ||

W 22/1 | (continued) | PS2 due | ||

F 24/1 | Billinear forms | §23 | ||

4 | M 27/1 | Tensor products | §24,§25 | Note on categories |

W 29/1 | (continued) | PS3 due | ||

F 31/1 | Review | |||

5 | M 3/2 | \Sym^n and \wedge^n | §29,§30 | |

W 5/2 | (continued) | |||

F 7/2 | Motivation | PS4 due; Feedback form | ||

6 | W 12/2 | The minimal polynomial | N 2.2.1 | |

F 14/2 | Generalized eigenspaces | N 2.2.2 | PS5 due | |

M 24/2 | Midterm exam | |||

7 | W 26/2 | Algebraic closure | N 2.2.3 | |

F 28/2 | Nilpotence | N 2.2.4 | PS6 due | |

8 | M 3/3 | Jordan blocks | N 2.2.4 | |

W 5/3 | Nilpotent Jordan form | N 2.2.4 | ||

F 7/3 | Jordan canonical form | N 2.2.5 | ||

9 | M 10/3 | Vector Norms | §86, N 3.1 | PS7 due |

W 12/3 | Matrix Norms | §87, N 3.2 | ||

F 14/3 | (continued) | |||

10 | M 17/3 | Power method | ||

W 19/3 | Completeness | PS8 due | ||

F 21/3 | Series | |||

10 | M 24/3 | Power series | ||

W 26/3 | Holomorphic calculus | PS9 due | ||

F 28/3 | Composition | |||

12 | M 31/3 | The Resolvent | ||

W 2/4 | ||||

F 4/4 | ||||

13 | M 7/4 | Review | PS10 due | |

M 16/4 | Final exam |

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