Linear Algebra module (MA22006)

Linear algebra is one of the most powerful branches of mathematics – and one of the most useful. It is at the heart of modern science, technology, and engineering.

It is the foundation for everything from solving systems of equations to building 3D graphics or training machine learning models.

In this module, you’ll explore what makes vector spaces so special and why they’re used everywhere from physics to computer science. You’ll learn how to represent mathematical objects and transformations using vectors, matrices, and linear maps.

You’ll also investigate the deeper structure of spaces. This includes what it means for vectors to be linearly independent, how to choose a basis, and how to use diagonalisation and the Cayley-Hamilton theorem to simplify complex problems.

Along the way, you'll gain experience with techniques like the Gram-Schmidt process and inner products. You'll build an intuitive understanding of geometry in higher dimensions.

If you want to master the language of modern maths and its real-world applications, this module is a crucial step.

What you will learn

In this module, you will:

• explore vector spaces and their properties in both geometric and abstract settings
• study linear independence, basis, and dimension
• learn about diagonalisation and the Cayley-Hamilton theorem
• apply the inner product and Gram-Schmidt process to construct orthogonal bases
• understand and visualise linear mappings as matrix transformations

By the end of this module, you will be able to:

• work confidently with vector spaces and subspaces
• determine linear independence and construct suitable bases
• use matrix methods to simplify problems and perform diagonalisation
• apply concepts like orthogonality and inner products in practical problems

Assignments / assessment

• Coursework (40%)
• Final written exam, two hours (60%)

Teaching methods / timetable

• Lectures
  • Core mathematical ideas introduced with theory and examples
• Tutorials
  • Guided sessions for problem-solving and collaborative learning