University of California, Berkeley

Spring 2008

This is an introductory course on linear algebra. We will study linear
algebra from both an abstract point-of-view with vector spaces and linear
transformations playing the central roles and also a more concrete
approach emphasizing matrices and vectors in **R**^{n}.
We will discuss some applications of linear algebra.

The official prerequisite for taking this course is Math 54: Linear algebra and differential equations.

- 05/16/08: Final exam will take place in 3108 Etcheverry Hall, 12:30–3:30, Thu, May 22.
- 05/16/08: Special office hours: 1–4, Wed, May 21.
- 05/07/08: Homework solutions brought up to date.
- 05/03/08: Revision lecture in Evans 75, 3:30–5, Tue, May 13.
- 05/03/08: Homework 9 posted. Due on Tue, May 13 (ie. during the revision lecture).
- 04/25/08: Homework 8 posted. Due in class on Thu, May 01.
- 04/22/08: Office hours on Thu, Apr 24, moved to 2–3:30.
- 04/18/08: Homework 7 posted. Due in class on Thu, Apr 24.
- 04/11/08: Homework 6 posted. Due in class on Thu, Apr 17.
- 04/04/08: Homework 5 posted. Due in class on Thu, Apr 10.
- 03/15/08: Office hours next week: 12–2, Mon, Mar 17; 2–3, Tue, Mar 18.
- 03/15/08: Solutions to Homework 4 posted.
- 03/12/08: Midterm will take place in 180 Tan Hall, 3:30–5, Tue, Mar 18.
- 03/12/08: Solutions to Homework 3 posted.
- 03/12/08: Solutions to Homework 2 posted.
- 03/10/08: Solutions to Homework 1 posted.
- 03/06/08: Homework 4 posted. Due in class on Thu, Mar 13.
- 02/28/08: Homework 3 posted. Due in class on Thu, Mar 06.
- 02/14/08: Homework 2 posted. Due in class on Thu, Feb 21.
- 02/07/08: Homework 1 posted. Due in class on Thu, Feb 14.
- 01/29/08: Handout 1 posted.
- 01/24/08: Office hours will formally begin next Thursday.
- 01/22/08: Check this page regularly for announcements.

**Location:** Evans Hall,
Room 75

**Times:** 3:30–5:00 PM on Tue/Thu

**Instructor:** Lek-Heng
Lim

Evans Hall, Room 873

`lekheng(at)math.berkeley.edu`

(510) 642-8576

Office hours Tuesday, 2:00–3:30 PM; Thursday, 1:00–2:30 PM.

**Graduate Student Instructor:** Charlie Smart

Evans Hall, Room 891

`smart(at)math.berkeley.edu`

Office hours 11:00 AM–4:00 PM every Wednesday and Thursday.

- Matrices
- Vector spaces
- Linear transformations
- Determinants
- Inner products
*QR*factorization- Linear functionals
- Eigenvectors
- Quadratic forms and Rayleigh's principle
- Jordan canonical form
- Applications
- Additional topics

Homework will be assigned once a week and will be due the following week (except possibly in the weeks when there is a midterm). Collaborations are permitted but you will need to write up your own solutions.

- Problem Set 9: PDF (posted: May 03; due: May 13); Solutions: PDF (posted: May 16)
- Problem Set 8: PDF (posted: Apr 25; due: May 01); Solutions: PDF (posted: May 07)
- Problem Set 7: PDF (posted: Apr 18; due: Apr 24); Solutions: PDF (posted: May 07)
- Problem Set 6: PDF (posted: Apr 11; due: Apr 17); Solutions: PDF (posted: May 05)
- Problem Set 5: PDF (posted: Apr 04; due: Apr 10); Solutions: PDF (posted: May 03)
- Problem Set 4: PDF (posted: Mar 06; due: Mar 13); Solutions: PDF (posted: Mar 15)
- Problem Set 3: PDF (posted: Feb 28; due: Mar 06); Solutions: PDF (posted: Mar 12)
- Problem Set 2: PDF (posted: Feb 14; due: Feb 21); Solutions: PDF (posted: Mar 12)
- Problem Set 1: PDF (posted: Feb 07; due: Feb 14); Solutions: PDF (posted: Mar 10)

**Bug report** on the problem sets or the solutions:
`lekheng(at)math.berkeley.edu`

- Handout 1 (posted: Jan 29).

- Course homepage from Fall 2007.

**Grade composition:** 40% Homework, 20% Midterm, 40% Final

Only the first book is required. The rest are optional supplementary references that you might like to check out from the library.

- Stephen Friedberg, Arnold Inse, and Lawrence Spence,
*Linear Algebra*, 4th Ed., Pearson Education, 2003.

- Gilbert Strang,
*Linear Algebra and its Applications*, 4th Ed., Thomson Learning, 2006.

- Lars Eldén,
*Matrix Methods in Data Mining and Pattern Recognition*, SIAM, 2006. Link

- Per Christian Hansen, Jim Nagy, and Dianne O'Leary,
*Deblurring Images: Matrices, Spectra, and Filtering*, SIAM, 2006. Link