- Offered for Year: 2022/23
- Module Leader(s): Dr David Kimsey
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
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 Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures - Present in Person |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision lectures - Present in Person |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes – Synchronous On-Line |
| Guided Independent Study | Independent study | 15 | 1:00 | 15:00 | Completion of in course assessments |
| Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Total | | | | 100:00 | |
Jointly Taught With
| Code |
Title |
|---|
| MAS3705 | Matrix 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 Examination | 120 | 1 | A | 80 | N/A |
Exam Pairings
| Module Code |
Module Title |
Semester |
Comment |
|---|
| MAS3705 | Matrix analysis | 1 | N/A |
Other Assessment
| Description |
Semester |
When Set |
Percentage |
Comment |
|---|
| Prob solv exercises | 1 | M | 10 | Coursework assignments |
| Prob solv exercises | 1 | M | 10 | Coursework 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
