Further Linear Algebra – LSE

Topics covered

• Diagonalisation and Jordan normal form, applied to systems of differential equations.
• Inner products, orthogonality, quadratic forms, and orthogonal diagonalisation.
• Direct sums and projections, with applications to least squares.
• Generalized inverses.
• Complex numbers. Complex matrices and vector spaces. Hermitian and unitary matrices, unitary diagonalisation and spectral decomposition.

Learning outcomes

If you complete the course successfully, you should be able to:

• Knowledge of the concepts, terminology, techniques and conventions covered in the half course.
• The ability to demonstrate an understanding of the underlying principles of the subject.
• The ability to demonstrate the ability to solve unseen mathematical problems involving an understanding of the concepts.