37233 Linear Algebra
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Subject handbook information prior to 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 35101 Introduction to Linear Dynamical Systems OR 37131 Introduction to Linear Dynamical Systems OR 33130 Mathematics 1 OR 33290 Statistics and Mathematics for Science
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 35212 Computational Linear Algebra
Description
In this subject, students develop an understanding of the theory of linear algebra, applications of linear algebra, and some of the main computational techniques used in these applications. Topics include systems of linear equations; linear spaces; basis and coordinate systems; linear transoformations; scalar product and orthogonality; Gram-Schmidt orthogonalisation, QR decomposition; least squares solutions; diagonalisation; singular value decomposition; and quadratic forms.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | apply skills in theoretical and computational techniques of linear algebra to solve substantial problems |
|---|---|
| 2. | understand, explain and prove the principal ideas and results which underpin the study of linear algebra |
| 3. | choose the most appropriate technique from those studied to solve a problem in linear algebra |
| 4. | contribute constructively and effectively to the collaborative discussions |
| 5. | implement appropriate hand-solving algorithms in linear algebra |
| 6. | prepare for real world applications of linear algebra |
| 7. | describe and apply relevant mathematical aspects of the use of linear algebra in professional practice |
| 8. | communicate clearly in the mathematical terminology of linear algebra |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate theoretical and technical knowledge of mathematical sciences including calculus, discrete mathematics, linear algebra, probability, statistics and quantitative management. (1.1)
- Evaluate mathematical and statistical approaches to problem solving, analysis, application, and critical thinking to make mathematical arguments, and conduct experiments based on analytical, numerical, statistical, algorithms to solve new problems. (2.1)
- Work autonomously or in teams to demonstrate professional and responsible analysis of real-life problems that require application of mathematics and statistics. (3.1)
- Design creative solutions to contemporary mathematical sciences-related issues by incorporating innovative methods, reflective practices and self-directed learning. (4.1)
- Use succinct and accurate presentation of reasoning and conclusions to communicate mathematical solutions, and their implications, to a variety of audiences, using a variety of approaches. (5.1)
Contribution to the development of graduate attributes
The ideas and techniques introduced in this subject are further developed and applied in a wide range of other subjects in the areas of differential equations, mathematical methods, optimisation and statistics, all of which underpin the professional and research practice of mathematical techniques. The subject is taught with an emphasis on fundamental basics as well as practical approaches, with the workshop classes and computer laboratories serving as an introduction to the routine use of the relevant approaches for solving mathematical problems, and also to develop skills for the use of computational systems in professional mathematical practice.
The subject contributes to strengthening the attributes of graduates in:
1. Disciplinary knowledge — through learning the fundamental and practical aspects
2. Research, inquiry and Critical Thinking — through critical and inquisitive research into problem solutions
3. Professional, Ethical and Social Responsibility — through maintaining academic intergrity
4. Reflection, Innovation, Creativity — through developing solutions for challenging problems
5. Communication — through clear and rigorous expression of the methodology
Teaching and learning strategies
Interactive workshops on-campus (2hpw) include lecture discussions. Tutorials (2hpw) are delivered on-campus. All the relevant teaching materials will be published on Canvas. It is recommended that classes each week should be supported by at least five hours per week of individual or group study. lndividual assignments are intended to provide ongoing training and feedback on the progress in the subject.
Content (topics)
- Systems of linear equations;
- Linear spaces and subspaces; linear dependence/independence;
- Basis, dimensions, coordinate systems;
- Linear transformations, eigenvectors and eigenvalues;
- Orthogonality, projections, orthogonalisation and orthogonal decomposition;
- Least-squares solutions;
- Quadratic forms;
- LU factorisation; iterative methods.
Assessment
Assessment task 1: Mid-term test
| Intent: | This assessment item addresses the following graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 5 and 8 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1, 4.1 and 5.1 |
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 40% |
| Length: | 2 hours on campus |
| Criteria: |
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Assessment task 2: Mastery tests
| Intent: | This assessment item addresses the following graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 4, 5 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1, 4.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 30% |
| Length: | 30 minutes each of the 8 tests |
| Criteria: |
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Assessment task 3: Final test
| Intent: | This assessment item addresses the following graduate attributes: 1. Disciplinary Knowledge. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 6 and 8 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1, 3.1, 4.1 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 30% |
| Length: | 2 hours, on campus |
| Criteria: |
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Minimum requirements
In order to pass this subject, a final result (the sum of all the marks with all the assessment tasks) of 50% or more must be achieved.
In addition, the major tests (assessment tasks 1 and 3) require collecting at least 40% of their available marks.
Recommended texts
Lay, D. C.: "Linear algebra and its applications" (e.g. 4th edition, Pearson, 2012).