MATH2501 - Linear Algebra

MATH2501 Linear Algebra is a second year course which develops and extends the work on vector spaces, linear transformations and eigenvalues begun in MATH1231.

These notes consist of twelve chapters, which cover the whole of the MATH2501 syllabus. Please note that those parts which are revision of first year topics – and the first six chapters contain quite a lot of these – do not consist of complete notes but of "background theory" questions and examples. The students and I worked through these parts interactively in classes. Topics which are new in second year receive a more detailed treatment. For more comprehensive information about the first year topics please see MATH1231.

• Chapter 1, Linear equations and matrices.
• Chapter 2, Vector spaces.
• Chapter 3, Linear transformations.
• Chapter 4, Least squares.
• Chapter 5, Determinants.
• Chapter 6, Eigenvalues, eigenvectors, diagonalisation.
• Chapter 7, Orthogonal transformations.
• Chapter 8, Symmetric matrices.
• Chapter 9, The Cayley–Hamilton theorem.
• Chapter 10, Jordan forms.
• Chapter 11, Functions of matrices.
• Chapter 12, Differential equations.