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Module

MAS3705 : Matrix analysis

  • Offered for Year: 2023/24
  • Module Leader(s): Dr David Kimsey
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System

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 ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Guided Independent StudyIndependent study151:0015:00Completion of in course assessments
Total100:00
Jointly Taught With
Code Title
MAS8705Matrix analysis
Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. 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
Matrix analysis1N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

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