Note that this material will not be examined.

Lecture 13
(Real) Quadratic Forms. Definition and example. Definition of positive definite and positive semi-definite. Properties of quadratic forms including (i) diagonalisation and (ii) positive definiteness.
Lecture 14
Application: statistical analysis of multivariate data ie. how to maximise a quadratic form given a constraint. Method and example.
Lecture 15 and 16
Summary of quadratic forms. Discussion of conic sections as applications of quadratic forms. Sylvester's inertia theorem.