Math 104


Applied Matrix Theory

 
 

Course meets Tuesdays and Thursdays, 12:50 - 2:05 in 320-105

Syllabus:

  1. 1.  Review of vectors, matrices, vector spaces and subspaces; matrices as linear transformations; rank of a matrix, linear independence and the four fundamental subspaces associated to a matrix.

  2. 2. Orthogonality and isometries.

  3. 3. The QR decomposition.

  4. 4. Spectral decomposition of a symmetrix matrix.

  5. 5. The singular value decomposition and its many applications, including least squares approximation, the condition number of a matrix, data compression.

  6. 6. Algorithms for solving linear systems and least squares problems.

  7. 7. Iterative methods for solving linear systems, incl. the conjugate gradient method.

  8. 8. Other applications, such as multivariate linear regression, principal component analysis.

Final Exam: Thursday March 21, 7-10PM

There will be weekly problem sets and one final exam. The final

grade will be computed from the problem sets and final exam

score at roughly a 60/40 ratio.

Both texts are on reserve in the library.


Further supplementary reading (handouts, etc.) will be announced in class and made available on this webpage

Text: Numerical Linear Algebra by L. Trefethen and D. Bau III

Another useful text is: Introduction to Linear Algebra

(4th Edition) by Gilbert Strang

Students are encouraged to work together on problem sets. However, you MUST write up your own work and cite all references (fellow students, books, websites) that you used. Failure to do so will not be looked on kindly.