MATH2601 Higher Linear Algebra

MATH2601 is a Mathematics Level II course; it is the higher version of MATH2501 Linear Algebra. See the course overview below.

Units of credit: 6

Prerequisites: MATH1231 or MATH1241 or MATH1251 or DPST1014, each with a mark of 70 or higher

Exclusions: MATH2501, MATH2099

Cycle of offering: Term 2 

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

MATH2601 (alternatively MATH2501) is a compulsory course for Mathematics and Statistics majors.

If you are currently enrolled in MATH2601, you can log into UNSW Moodle for this course.

Course Aims

The principal aim of this subject is for students to develop a working knowledge of the central ideas of linear algebra: vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, canonical forms and applications of these ideas in science and engineering.

In particular, the course introduces students to one of the major themes of modern mathematics: classification of structures and objects. Using linear algebra as a model, we will look at techniques that allow us to tell when two apparently different objects can be treated as if they were the same. A secondary aim is to understand how certain calculations in linear algebra can be thought of as algorithms, that is, as fixed methods which will lead in finite time to solutions of whole classes of problems. Additionally, there will be a focus on writing clear mathematical proofs.

Course Description

The course begins with a revision of vector spaces, linear transformations and change of basis. It also covers inner products over both the real and complex fields, orthogonalization, reflections, QR factorizations unitary, self adjoint and normal transformations. It then turns to the study of eigenvalues and eigenvectors, diagonalization, Jordan forms and functions of matrices. The course also includes applications to linear systems of differential equations, quadratics and rotations. Where content is in common with MATH2501, this course aims to give students a deeper level of understanding.