Matrices and Complex Numbers

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 5
Thursday 03 October 2019
Saturday 14 December 2019
01 October 2019


Requisites for this module


EC114, MA201, MA204, MA205, MA225, MA301, MA306, MA314, MA317

Key module for

BSC I1G3 Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year)

Module description

This module introduces students to the basics of linear algebra, emphasising vectors and matrices.

Module aims

The aim of this module is to provide BSc Data Science and Analytics students with basics of linear algebra, emphasising vectors and matrices.

Module learning outcomes

On completion of the module students should be able to: understand the geometric and algebraic properties of vectors in two- and three-dimensional
Euclidean space; perform simple operations on matrices; solve systems of linear equations using row operations; calculate the determinant and the inverse of a matrix; calculate the eigenvalues and eigenvectors of a matrix; diagonalize a symmetric matrix; understand linear mappings, projection matrices, singular value decomposition of quadratic forms; apply linear mappings, projection matrices, singular value decomposition of quadratic forms using data science software such as R or Python.

Module information


Complex numbers:

- Addition, subtraction, multiplication and division of complex numbers in both Cartesian and polar form;
- de Moivre's theorem;
- complex nth roots.


- Geometry and algebra of R2 and R3;
- vector addition and scalar multiplication.


- matrix addition and multiplication, scalar multiplication;
- systems of linear equations;
- Gaussian elimination, elementary row operations;
- identity and inverse matrices, determinants;
- eigenvalues and eigenvectors;
- diagonalization of symmetric matrices;
- applications to quadratic forms in two and three dimensions;
- matrices of linear mappings;
- projection matrices;
- singular value decomposition of quadratic forms.

Learning and teaching methods

This module consists of 20 lectures, 10 classes and five labs. There are three revision lectures in the Summer term.


This module does not appear to have a published bibliography.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework E-assessment 1 50%
Coursework E-assessment 2 50%
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Alexei Vernitski, email
Dr Alexei Vernitski (



External examiner

No external examiner information available for this module.
Available via Moodle
Of 64 hours, 13 (20.3%) hours available to students:
51 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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