# MTH2025 - Linear algebra (advanced) - 2019

## Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Coordinator(s)

Unit guides

Offered

Clayton

• First semester 2019 (On-campus)

Prerequisites

A High Distinction in MTH1030 or ENG1005, or a Distinction in MTH1035, or by approval of the Head of School of Mathematical Sciences. In order to enrol in this unit students will need to apply via the Science Student Services officeScience Student Services office (https://www.monash.edu/science/current-students/admissionsstudy-optionsinternal-transfer_arch).

Prohibitions

MTH2021

## Synopsis

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.

## Outcomes

On completion of this unit students will be able to:

1. Understand 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. Understand 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

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for both the end-of-semester examination and continuous assessment components.

## Workload requirements

Three 1-hour lectures, one 1-hour workshop and one 2-hour applied class per week

See also Unit timetable information