# MATH40550 Applied Matrix Theory

This module is designed to develop an understanding of selected topics from matrix theory, that are particularly relevant in applications. The students are introduced to matrix theoretical concepts such as matrix norms, singular values, and various matrix factorisations. They learn about different classes of matrices such as symmetric, orthogonal, positive semidefinite, sparse, and how different matrix properties can be exploited in applications.

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Curricular information is subject to change

Learning Outcomes:

On completion of this course, the students should have a firm grasp of various matrix theoretical methods and matrix properties. They should be able to perform calculations for small matrices on paper and for large matrices with the aid of a computer. They should be able to understand how different concepts are derived (proofs of theorems), and how they are relevant in applications.

Indicative Module Content:

Provisional Module Structure

1 - Basic Concepts: Eigenvalues, Eigenvectors, and Similarity

2 - Norms for Vectors and Matrices

3- Schur Factorisation and Singular Value Decomposition

4 -Conditioning and perturbation theorems

5- Positive Definite Matrices

Student Effort Hours:
Student Effort Type Hours
Specified Learning Activities

24

Autonomous Student Learning

46

Lectures

18

Tutorial

12

Total

100

Approaches to Teaching and Learning:
Lectures,
Flipped classroom (some lecture hours might be transformed in Q&A sessions)
Enquiry and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Requirements:

The students are expected to have an intermediate level of linear algebra. They should have a good grasp of linear algebraic concepts such as vector space, linear independence and basis. They should be competent in solving linear systems, and preforming matrix operations such as computing determinants, inverses and eigenvalues.

Module Requisites and Incompatibles
Not applicable to this module.

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: Assessment may include a timed examination. Varies over the Trimester n/a Alternative linear conversion grade scale 40% No

30

No
Examination: End of Trimester Exam 2 hour End of Trimester Exam No Alternative linear conversion grade scale 40% No

70

No

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour