Mathematics

Linear Algebra 2

Module code: G5138
Level 4
15 credits in spring semester
Teaching method: Lecture, Workshop
Assessment modes: Coursework, Unseen examination

 

Linear Algebra 2 follows on from Linear Algebra 1 by extending the geometrical concepts into more abstract settings. For example, you have seen vectors as geometrical objects in two- or three-dimensional space in Linear Algebra 1, but we can now generalise the concept of a vector space to a more abstract setting.

Similarly, examples of linear transformations are rotations or multiplication of vectors by a scalar; again, this can be defined in a more general setting and be characterised by the multiplication with a matrix.

When given a linear transformation, we would like to identify certain directions that are multiplied by a certain scalar, this leads to the definition of eigenvectors and eigenvalues, which are important concepts that you will encounter in other modules in higher years.

Module learning outcomes

• Appreciate the structure of vectors spaces as abstract objects;
• Understand the properties of linear transformations between vector spaces and their matrices;
• Demonstrate working knowledge of calculating eigenvalues/eigenvectors, and vectors/matrices in different bases.