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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
Textbooks:
- 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)
These books are on reserve at the Math/CS library.
Handouts:
All handouts will be posted online.
Course assistant and office hours:
Xiaodong Li () MTu 1p-2p and Th 7p-8p
Room 380-T
Grading:
- Homework assignments: 50%
- Homework assignments will generally be distributed on
Wednesdays and are due in class the following
Wednesday.
- 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 December 7, 12:15-3:15 p.m.
- 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.
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