Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 167: Applied Linear Algebra
Approved: 2008-04-15, Naoki Saito, Roland Freund, Hong Xiao

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Gilbert Strang: Linear Algebra and Its Applications, 4th Ed., Brooks/Cole, 2006. ($80)
Search by ISBN on Amazon: 978-0030105678

Prerequisites:

22A (Linear Algebra) or 67 (Modern Linear Algebra)

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1st Week

From various sources (see note below)

What is Applied Linear Algebra? Motivational introduction with examples

2nd Week

Sec. 1.4-1.6

Systems of linear algebraic equations, LU factorization and its applications

3rd Week

Sec.2.1-2.3, 2.6

Vector spaces, subspaces, bases, linear transformations

4th Week

Sec. 3.1, 3.2, 3.4

Orthogonality. QR factorization and Gram-Schmidt process I.

5th Week

Sec. 3.3; Midterm Exam

Orthogonality. QR factorization and Gram-Schmidt process II. Applications to least squares problems

6th Week

Sec. 5.1-5.3

Eigenvalue decomposition and its applications I

7th Week

Sec.5.4-5.6

Eigenvalue decomposition and its applications II

8th Week

Sec. 6.3 with extra material

Singular value decomposition and its applications I

9th Week

Sec. 6.3 with extra material

Singular value decomposition and its applications II

10th Week

Some appropriate sections from the text as well as extra material, handouts

Other applications (see notes below)

Additional Notes:

• Basic concepts of linear algebra (22A or 67) are assumed and will not be reviewed in the class. The instructor should explicitly inform the enrolled students of this requirement.
• Knowledge of programming language is required. A certain number of programming projects will be assigned in the course. Applications of least squares, eigenvalue decomposition, singular value decomposition form good programming projects.
• In the 1st Week, it is important to motivate the students using important examples to show how linear algebra is used in real world. Suggested examples are: image compression, web search engines, inverse problems (e.g., tomography), etc.
• In the 8th and 9th Weeks, the instructor should supply some applications of SVD including web search engines, least squares problems, image approximations, inverse problems in a more details manner some of which were discussed in the 1st Week.
• In the 10th Week, an instructor can freely choose various applications of interest. Examples are:Sec. 2.5 Graphs and Networks;Sec. 3.5 The Fast Fourier Transform;Sec. 6.1-6.2 Positive Definite MatricesSec. 8.2 The Simplex Method and Karmarkar's Method.

Other possible sources of material are:

− Carl D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM, 2000.
− Lloyd. N. Trefethen and Davis Bau, III: Numerical Linear Algebra, SIAM, 1997.
− Michael W. Berry and Murray Browne: Understanding Search Engines: Mathematical Modeling and Text Retrieval, 2nd Ed., SIAM, 2005.