Singapore University of Social Sciences

MTH208e Advanced Linear Algebra introduces the abstract notion of field while providing concrete examples of linear algebra over the field of real numbers and the field of complex numbers. The course proceeds to focus on the Jordan canonical form. The main results on the existence and uniqueness of Jordan canonical form will be presented without proof. The course also defines the adjoint of a linear operator and normal operators and establishes the main results on normal operators, specialising to the cases of self-adjoint operators, orthogonal operators and unitary operators. Finally, the course ends with a discussion of symmetric bilinear forms and alternating bilinear forms.