Global Opportunities

MAS3705 : Matrix analysis

Semesters
Semester 1 Credit Value: 10
ECTS Credits: 5.0

Aims

To equip students with a range of tools and methods for diagonalising and factorising matrices. To understand these techniques and applications that arise both in pure and applied sciences. To reinforce the ability of students to identify real-life problems that can be solved with matrices.

Module summary

Matrices play a key role in mathematics with many applications to pure, statistics and physics. They are necessary in almost every area of science, whether it be mathematics, economics, engineering or operational research. Matrix analysis provides a common framework to this effect. It allows the development of design tools and algorithms that solve efficiently linear systems, polynomial matrix equations, optimization problems, as well as problems that arise in quantum information theory. In this course we focus on key results that enable the combination of linear algebra with mathematical analysis. By the end of the course the students will understand classical and recent results of matrix analysis that have proved to be important to pure and applied mathematics.

Outline Of Syllabus

Matrix factorisations (Jordan normal form, polar decomposition, singular value decomposition etc.). Similarity classes of matrices. Hermitian matrices and positive definite matrices. Spectral theorems for normal matrices and various subclasses. Perron-Frobenius Theorem.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures - Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes – Synchronous On-Line
Guided Independent StudyIndependent study151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Total100:00
Jointly Taught With
Code Title
MAS8705Matrix analysis
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A80N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS8705Matrix analysis1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Coursework assignments
Prob solv exercises1M10Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable