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: matrixmatrix and matrixvector
multiplications
 partial derivatives and the chain rule of vector calculus
 definition of eigenvalue and eigenvector
 3by3 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 leastsquares problems
 Iterative methods for solving linear systems:
the method of conjugate gradients
 Applications: multivariate linear regression and principal
component analysis
Textbooks:
 Numerical Linear Algebra by LLoyd N. Trefethen and David
Bau, III, SIAM (required)
 Introduction to Linear Algebra
by Gilbert Strang, WellesleyCambridge 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 1:303 and W 1:303, room 380383YY. Mahdi Soltanolkotabi
() Tu 5:307 and W 56:30, room 380380U
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
writeup.
 Final exam: 50%.
 In accordance with University scheduling, the endQuarter
examination is scheduled for March 22, 7:0010:00 p.m., room
200002.
 We will have an openbook, opennotes exam.
Course policies:
 Use of sources (people, books, internet and so on)
without citing them in homework sets results in failing
grade for course.
