University of California, Berkeley

Fall 2007

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.

- 12/11/07: Final exam will take place in 141 McCone Hall, 12:30–3:30, Thu, Dec 13.
- 12/11/07: Extra office hours 12–2 on Wed, Dec 12.
- 12/10/07: Solutions to Homeworks 10 posted.
- 12/09/07: Solutions to Homeworks 9 posted.
- 12/05/07: Extra office hours 12–2 on Fri, Dec 07.
- 12/05/07: GSI's review session 12–5 on Sun, Dec 09 in Evans 60.
- 12/04/07: Homework 10 posted. Due in class on Mon, Dec 10.
- 12/02/07: Solutions to Homeworks 8 posted.
- 11/27/07: Homework 9 posted. Due in class on Mon, Dec 3.
- 11/17/07: GSI will not hold office hours this week, so I will have extended office hours 12–4 on Mon, Nov 19.
- 11/15/07: Homework 8 posted. Due in class on Wed, Nov 21.
- 11/05/07: Extra office hours 12–1 on Tue, Nov 06.
- 11/04/07: Solutions to Homeworks 6 and 7 posted.
- 10/29/07: GSI's new office hours: Wed and Thu, 12–5 (with the exception of 4–6 on Nov 14 and 10–6 on Nov 15).
- 10/28/07: Solutions to Homeworks 5 posted.
- 10/27/07: Homework 7 posted. Due in class on Fri, Nov 2.
- 10/24/07: Midterm II will take place in 126 Barrows Hall, 11–12, Wed, Nov 07.
- 10/20/07: Homework 6 posted. Due in class on Fri, Oct 26.
- 10/18/07: Solutions to Homeworks 3 and 4 posted.
- 10/13/07: Homework 5 posted. Due in class on Fri, Oct 19.
- 10/07/07: Homework 4 posted. Due in class on Fri, Oct 12.
- 09/29/07: Homework 3 posted. Due in class on Fri, Oct 5.
- 09/24/07: This Wed's office hours brought forward to 11–1, Tue, Sep 25. Office hours will go back to normal after midterm.
- 09/23/07: Solutions to Homeworks 1 and 2 posted.
- 09/23/07: Here's a handout that may be useful for the midterm.
- 09/19/07: Midterm I will take place in 155 Donner Lab, 11–12, Wed, Sep 26.
- 09/17/07: The GSI's office hours this week have been changed to Wed 10–6 and Thu 11–1.
- 09/15/07: Homework 2 posted. Due in class on Fri, Sep 21.
- 09/07/07: Homework 1 posted. Due in class on Fri, Sep 14.
- 08/30/07: This class is currently oversubscribed. Prof. Benoit Dherin will teach the same class at the same time (11–12, MWF) in Etcheverry 3107. Please attend his lectures instead if you are still on the waiting list for my class.
- 08/27/07: Check this page regularly for announcements.

**Location:** Evans Hall,
Room 71

**Times:** 11:00 AM–12:00 PM on Mon/Wed/Fri

**Instructor:** Lek-Heng
Lim

Evans Hall, Room 873

`lekheng(at)math.berkeley.edu`

(510) 642-8576

Office hours 12:00–2:00 PM every Monday and
2:00–4:00 PM every Wednesday

**Graduate Student Instructor:** Janak Ramakrishnan

Evans Hall, Room 1043

`janak(at)math.berkeley.edu`

Office hours 12:00–5:00 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 10: PDF (posted: Dec 4; due: Dec 10); Solutions: PDF (posted: Dec 10)
- Problem Set 9: PDF (posted: Nov 27; due: Dec 3); Solutions: PDF (posted: Dec 09)
- Problem Set 8: PDF (posted: Nov 15; due: Nov 21); Solutions: PDF (posted: Dec 02)
- Problem Set 7: PDF (posted: Oct 27; due: Nov 02); Solutions: PDF (posted: Nov 04)
- Problem Set 6: PDF (posted: Oct 20; due: Oct 26); Solutions: PDF (posted: Nov 04)
- Problem Set 5: PDF (posted: Oct 13; due: Oct 19); Solutions: PDF (posted: Oct 28)
- Problem Set 4: PDF (posted: Oct 07; due: Oct 12); Solutions: PDF (posted: Oct 18)
- Problem Set 3: PDF (posted: Sep 29; due: Oct 05); Solutions: PDF (posted: Oct 18)
- Problem Set 2: PDF (posted: Sep 15; due: Sep 21); Solutions: PDF (posted: Sep 23)
- Problem Set 1: PDF (posted: Sep 07; due: Sep 14); Solutions: PDF (posted: Sep 23)

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

- Check out Timothy Gowers's blog entry on "How should vector spaces be introduced?" and also "The exchange lemma and Gaussian elimination". Don't forget to take a look at the comments section for Terence Tao's response.

- Handout 1: List of field and vector space axioms PDF (posted: Sep 23)

**Midterm II grade distribution:** median = 30,
mean = 30, max = 40, min = 12, stdev = 7.7, max possible marks = 40.

**Midterm I grade distribution:** median = 35,
mean = 36, max = 50, min = 21, stdev = 6.6, max possible marks = 50.

**Grade composition:** 40% Homework, 15% Midterm I, 15%
Midterm II, 30% Final

The second book is optional. It is an elementary version of the first, going more slowly and providing somewhat more details and examples.

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

- Gilbert Strang,
*Introduction to Linear Algebra*, 3rd Ed., Wellesley-Cambridge, 2003.

Next semester's class will see even more cool applications. The following books will be used in Spring 2008.

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

- P.C. Hansen, J.G. Nagy, and D.P. O'Leary,
*Deblurring Images: Matrices, Spectra, and Filtering*, SIAM, 2006. Link