MTH2025 Linear algebra (advanced)

When you finish this unit, you should be able to:

1. 1

   Apply concepts related to vector spaces, including subspace, span, linear independence and basis;

2. 2

   Understand properties of linear transformations and identify their kernel and range;

3. 3

   Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;

4. 4

   Understand matrix decomposition techniques;

5. 5

   Understand concepts related to inner product spaces and apply these to problems such as least-squares data fitting;

6. 6

   Develop and apply tools from linear algebra to a wide variety of relevant situations;

7. 7

   Recognise and apply relevant numerical methods and demonstrate computational skills in linear algebra;

8. 8

   Present clear mathematical arguments in both written and oral forms;

9. 9

   Develop and present rigorous mathematical proofs.