Description
This course is an introduction to matrix analysis, developing essential
tools such as the Jordan canonical form, Perron–Frobenius theory, the
singular value decomposition, and matrix functions.
It builds on the first year linear algebra course.
Apart from being used in many areas by almost all mathematicians,
matrix analysis has broad
applications in fields such as engineering, physics, statistics, econometrics
and data mining, and examples from some of these areas will be used to
illustrate and motivate some of the theorems developed in the course.
This course is part of the
Numerical Analysis Pathway.
Prerequisites
MATH10202 and MATH10212 (Linear Algebra)
Class Test
The test will took place during the Wednesday lecture on 11th November, 2015, in Stopford Theatre 2 and 6.
A
sample test is available together with
sample solutions.
Calculators and notes are not permitted.
Midterm feedback is available.
Final Test
The final test will take place on January 18th at 14:00.
(This time may change. For confirmation and location, please check your exam timetable in January.)
The duration of the test is 2 hours. It consists of two sections, Section A (answer all 5 questions)
and Section B (answer 2 out of 3 questions). If more than 2 questions from Section B are attempted,
the first 2 answers will be marked.
Past exam papers are available
from this website.
Calculators are
not permitted.
For the final test
all material will be examinable, with the exception of the following:
- Theory of Eigensystems: Section 2.3.1 on the Structure of a Jordan Matrix; Exercises 12, 18, 19.
- Norms: The part [<==] of the proof of Theorem 3 (however, you should know the proof of the [==>] direction); Exercises 7, 12.
- Generalized Inverses and the SVD: Proof of Theorem 2.
- Perron-Frobenius Theory: Proof of Theorem 3; Exercises 2, 4, and 6.
Handouts and exercises will be posted here as we progress on the course.
Note that these
handouts do not substitute regular attendance to the course. In particular,
illustrating examples and proofs of theorems are given in the lectures only.
Handouts and Exercises
Solutions to Exercises
The solutions of most exercises will be discussed in the feedback session.
For your reference, the solutions are also available for download as soon
as we finish with a corresponding chapter.
Optional Material
Here you will find the slides I use in the lectures. Note that there is no need to print these
slides as they are just a condensed version of the handouts (see above). You may download
and try out some of the Matlab demos I give in the lectures.
General information