Overview

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. Linear functionals and dual spaces. Matrix decompositions, least squares approximation, power method. Applications to areas such as coding, economics, networks, graph theory, geometry, dynamical systems, Markov chains, differential equations.

Offerings

S1-01-CLAYTON-ON-CAMPUS
S1-FF-CLAYTON-FLEXIBLE

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Tim Garoni

Unit Coordinator(s)

Associate Professor Tim Garoni

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Apply concepts related to vector spaces, including subspace, span, linear independence and basis;

2.

Understand properties of linear transformations and identify their kernel and range;

3.

Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;

4.

Understand matrix decomposition techniques;

5.

Understand concepts related to inner product spaces and apply these to problems such as least-squares data fitting;

6.

Develop and apply tools from linear algebra to a wide variety of relevant situations;

7.

Recognise and apply relevant numerical methods and demonstrate computational skills in linear algebra;

8.

Present clear mathematical arguments in both written and oral forms;

9.

Develop and present rigorous mathematical proofs.

Assessment summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: If you would otherwise have passed the unit but you do not achieve at least 45% in the end of semester written examination and continuous assessment you will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Workload requirements

Workload

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (unit course reader, printing, stationery) - $120.

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics