MATRIX ANALYSIS - 2020/1
Module code: MAT3045
This module continues to develop the theory of matrices initiated in MAT1034 Linear Algebra, and introduces concepts of convergence and distance to the study of matrices. The module then progresses through several advanced topics in linear algebra such as the Perron-Frobenius theorem, tensors and exterior powers of matrices, and singular value decompositions. As an application we will investigate the PageRank algorithm used by Google to rank web pages.
MORRIS Ian (Maths)
Number of Credits: 15
ECTS Credits: 7.5
Framework: FHEQ Level 6
JACs code: G100
Module cap (Maximum number of students): N/A
Prerequisites / Co-requisites
Linear Algebra, Real Analysis 2.
Indicative content includes:
The Jordan normal form
Norms; equivalence of norms in finite dimensions; convergence of sequences and series of matrices; operator norms
The singular value decomposition
The spectral radius formula and Yamamoto's theorem
Positivity and the Perron-Frobenius theorem
The PageRank algorithm
Tensors and exterior powers of matrices
|Assessment type||Unit of assessment||Weighting|
|School-timetabled exam/test||CLASS TEST (50 MINS)||20|
The assessment strategy is designed to provide students with the opportunity to demonstrate:
Understanding of and ability to interpret and manipulate mathematical statements.
Subject knowledge through the recall of key definitions, theorems and their proofs.
Analytical ability through the solution of unseen problems in the test and exam.
Thus, the summative assessment for this module consists of:
One two hour examination at the end of Semester 2; worth 80% module mark.
One 50 minute class test; worth 20% module mark
Formative assessment and feedback
Students receive written feedback via a number of marked coursework assignments over an 11 week period. In addition, verbal feedback is provided by lecturer at biweekly tutorial lectures.
- Extend and deepen students' understanding of linear maps on finite-dimensional spaces
- Familiarise students with important matrix decompositions, such as the Jordan form and singular value decomposition
- Familiarise students with core topics in the analysis of matrices such as convergence, norms and the Perron-Frobenius theorem
- Introduce students to tensor and exterior algebra of matrices
|001||Rigorously interpret convergence and infinite summation of matrices, including matrix exponentials||KC|
|002||Define and calculate singular values, Kronecker products and exterior powers, at least in simple cases||KC|
|003||Understand the interaction between the norm/singular values of a matrix or matrices and the tensor / exterior product||KC|
|004||Understand the significance of positivity and the Perron-Frobenius theorem.|
|005||Define the determinant using exterior algebra and derive its essential properties||KC|
C - Cognitive/analytical
K - Subject knowledge
T - Transferable skills
P - Professional/Practical skills
Overall student workload
Independent Study Hours: 117
Lecture Hours: 33
Methods of Teaching / Learning
The learning and teaching strategy is designed to provide:
An introduction to analytic methods in linear algebra and their applications.
The learning and teaching methods include:
3 x 1 hour lectures per week x 11 weeks, with additional notes on white board to supplement the module handbook and Q + A opportunities for students.
(every second week) 1 x 1 hour tutorial replaces one of the lectures for guided discussion of solutions to problem sheets provided to and worked on by students during the tutorial.
Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.
Programmes this module appears in
|Mathematics MSc||1||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics with Statistics BSc (Hons)||1||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics BSc (Hons)||1||Optional||A weighted aggregate mark of 40% is required to pass the module|
|Mathematics MMath||1||Optional||A weighted aggregate mark of 40% is required to pass the module|
Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2020/1 academic year.