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
- vector operations: dot product, cross product
- matrix operations: matrix-matrix and matrix-vector
- 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.
- 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
- The singular value decomposition and its
- 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
These books are on reserve at the Math/CS library.
- Numerical Linear Algebra by LLoyd N. Trefethen and David
Bau, III, SIAM (required)
- Introduction to Linear Algebra
by Gilbert Strang, Wellesley-Cambridge Press, 4th edition (optional)
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
- Homework assignments: 50%
- Homework assignments will generally be distributed on
Thursdays and are due in class the following
- 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
- Final exam: 50%.
- In accordance with University scheduling, the end-Quarter
examination is scheduled for March 22, 7:00-10:00 p.m., room
- We will have an open-book, open-notes exam.
- Use of sources (people, books, internet and so on)
without citing them in homework sets results in failing
grade for course.