# Advanced Linear Algebra

Queensland University of Technology

## Course Description

• ### Host University

Queensland University of Technology

• ### Location

Brisbane, Australia

Algebra

• ### Language Level

Taught In English

• ### Prerequisites

(MXB102 or MAB461) and (MXB106 or MAB112 or MAB122)

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credit Points

12
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

The main aim of this unit, which is intended for students majoring in mathematics and students in other courses who require the foundations of linear algebra, is to develop the theory of linear algebra and to provide you with the necessary skills to apply this theory in science, technology, engineering and mathematics. It seeks to foster an appreciation of the historical development and the value of the principles and methods presented. You will also be well prepared for later studies in computational mathematics.

Learning Outcomes
On successful completion of this unit you should be able to:

1. Apply specific methods, concepts and techniques of linear algebra to solve abstract and real world problems.
2. Present mathematical arguments clearly and logically both in written form and orally.
3. Use mathematical software to explore and solve problems in linear algebra.
4. Actively participate in team-based activities.

Content
The mathematical content of the unit will include topics that will be selected from the following three sections:
Revision of set theory and abstract mathematics; A brief introduction to the Euclidean space R^n; review of key matrix properties, facts about linear systems and the properties of matrix inverses; the notions of vector subspaces, spanning sets, linear independence, basis and dimension in R^n; rank and nullity, the general solution of a linear system of equations; the eigenvalue problem within the Euclidean space framework; matrix diagonalisation; and computing matrix functions.
Arbitrary Vector Spaces: properties and structure of a general, arbitrary vector space; properties of vector subspaces; a brief introduction to linear transformations and change of basis.
Inner Product Spaces: inner products; orthogonality; orthonormal bases; vector norms; Gram-Schmidt Process and QR-Decomposition; orthogonal projections; Singular Value Decomposition,best approximation and least squares solutions; data fitting.

Group work strategies that expand upon those discussed in first year studies will also be explored to prepare you for group assessment work. This will include consideration of activity planning and how individuals and groups function together. The standards for presentation and communication of mathematical and statistical information at this level of study will be discussed and demonstrated by example.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.