Math 104
Applied Matrix Theory
Winter 2011



Instructor
Emmanuel Candes
113 Sequoia Hall

Office Hours: M 11-12, F 1:30-2:30
or by appointment

   

Lectures
Tuesday, Thursday
2:15-3:30 p.m.
Room: 380-381T

 

Home

Handouts

Homework


Description: The aim of this course is to introduce the key mathematical ideas in matrix theory, which are used in modern methods of data analysis, scientific computing, optimization, and merely all quantitative fields of science and engineering. While the choice of topics is motivated by their use in various disciplines, the course will emphasize the theoretical and conceptual underpinnings of this subject, just as in other (applied) mathematics course.


Prerequisite:
Math 51, and either Math 52 or Math 53. Alternatively, familiarity with the following notions:

  • vector operations: dot product, cross product
  • matrix operations: matrix-matrix and matrix-vector multiplications
  • partial derivatives and the chain rule of vector calculus
  • definition of eigenvalue and eigenvector
  • 3-by-3 determinants

No knowledge of computer programming is necessary.


Syllabus:

  • Matrices, vectors and their products (review)
  • Matrices as linear transformations
  • Rank of a matrix, linear independence and the four fundamental subspaces of a matrix
  • Orthogonality and isometries
  • The QR decomposition
  • Eigenvalues and the spectral decomposition of symmetric matrices
  • The singular value decomposition and its applications
  • The conditioning of a matrix
  • Least squares problems
  • Algorithms for solving systems of linear equations and least-squares problems
  • Iterative methods for solving linear systems: the method of conjugate gradients
  • Applications: multivariate linear regression and principal component analysis


Textbooks:

  1. Numerical Linear Algebra by LLoyd N. Trefethen and David Bau, III, SIAM (required)
  2. Introduction to Linear Algebra by Gilbert Strang, Wellesley-Cambridge Press, 4th edition (optional)
These books are on reserve at the Math/CS library.

Handouts: All handouts will be posted online.

Course assistant and office hours: Laurence Nedelec () M 1:30-3 and W 1:30-3, room 380-383YY. Mahdi Soltanolkotabi () Tu 5:30-7 and W 5-6:30, room 380-380U

Grading:

  • Homework assignments: 50%
    • Homework assignments will generally be distributed on Thursdays and are due in class the following Thursday.
    • Late homeworks will NOT be accepted for grading (medical emergencies excepted with proof).
    • There will be about 7 assignments; the lowest score will be dropped in the final grade.
    • It is encouraged to discuss the problem sets with others, but everyone needs to turn in a unique personal write-up.

  • Final exam: 50%.
    • In accordance with University scheduling, the end-Quarter examination is scheduled for March 22, 7:00-10:00 p.m., room 200-002.
    • We will have an open-book, open-notes exam.

Course policies:

  • Use of sources (people, books, internet and so on) without citing them in homework sets results in failing grade for course.