Matrices and Complex Numbers

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 5
Thursday 03 October 2019
Saturday 14 December 2019
09 April 2020


Requisites for this module


EC114, MA201, MA204, MA205, MA225, MA301, MA306, MA314, MA315, 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

The module introduces several important mathematical constructions, namely, complex numbers, vectors and matrices, and shows how they are employed in various areas of mathematics and statistics. Particular attention is paid to how matrices are used for data analytics.

Module aims

The aim of this module is to introduce BSc Data Science and Analytics to several important mathematical constructions, namely, complex numbers, vectors and matrices, and show how matrices are used for data analytics.

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 Matlab; be able to add, subtract, multiply, and divide complex numbers in Cartesian form; be able to plot complex numbers on an Argand diagram; be able to move between Cartesian and polar forms of complex numbers; be able to calculate arguments, moduli and complex conjugates; be able to multiply and divide complex numbers in polar form; be able to find complex nth roots

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 vectors in 2 & 3 dimensions;
- vector addition and scalar multiplication.


- matrix addition and 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 one lecture and two labs per week which are shared with MA114-4, and one extra lab in each of the last five weeks of the term. There are four revision lectures in the summer term.


This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   E-assessment 1      
Coursework   E-assessment 2      
Exam  1440 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, email
Dr Alexei Vernitski (



External examiner

No external examiner information available for this module.
Available via Moodle
Of 137 hours, 10 (7.3%) hours available to students:
127 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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