What is this course about?

This module offers an introduction to linear algebra which is essentially a set of notational conventions and operations which allow you to manipulate large systems of equations conveniently.

There are five sections in this course:

  1. Introduction to Linear Algebra
  2. Vectors
  3. Matrices
  4. Linear Mappings through matrices
  5. Eigenvalues and eigenvectors - application to data problems

The course focuses on building your intuition about vectors and translations through the use of quizzes and interactive widgets as well as occasionally asking you to fill in the gaps in some Python coding examples. In the final section, you will learn how linear algebra is at the heart of Google's famous page rank algorithm, which is used for deciding the order of web pages in search results.

What are the learning outcomes?

Introduction to linear algebra:

  • Recall how machine learning and vectors and matrices are related
  • Interpret how changes in the model parameters affect the quality of the fit to the training data
  • Recognize that variations in the model parameters are vectors on the response surface - that vectors are a generic concept not limited to a physical real space
  • Use substitution / elimination to solve a fairly easy linear algebra problem
  • Understand how to add vectors and multiply by a scalar number


  • Calculate basic operations (dot product, modulus, negation) on vectors
  • Calculate a change of basis
  • Recall linear independence
  • Identify a linearly independent basis and relate this to the dimensionality of the space


  • Understand what a matrix is and how it corresponds to a transformation.
  • Explain and calculate inverse and determinant of matrices
  • Identify and explain how to find inverses computationally and what goes wrong.

Linear mappings through matrices:

  • Identify matrices as operators
  • Relate the transformation matrix to a set of new basis vectors
  • Formulate code for mappings based on these transformation matrices
  • Write code to find an orthonormal basis set computationally

Eigenvalues and eigenvectors - application to data problems:

  • Identify geometrically what an eigenvector/value is
  • Apply mathematical formulation in simple cases
  • Build an intuition of larger dimension eigensystems
  • Write code to solve a large dimensional eigen problem

Who is this course aimed at?

Any students from all undergraduate Science and Engineering degrees. Please note that you should be comfortable in your A-Level Maths before you start this course as it is designed to challenge you.

How will this course be delivered?

This is an asynchronous module and will be delivered online, via the Coursera platform. Please visit the links to courses tab in your Microsoft Teams space for information on how to get started.

How much time will the course take up?

The course is designed to take up a total of approximately 19 hours, to be distributed according to your own preference.