Linear Algebra

Course aim

To develop basic concepts in linear algebra and apply them to problems using analytic and numerical techniques. To provide an introduction to matrix algebra and to use the software package MATLAB to solve problems.

Course content

Module 1: Linear Algebra (Applied)

Vectors and matrices, linear dependence of vectors, linear systems of equations, row operation as matrix multiplications, row reduced echelon form (RREF), matrix inverse, determinants, eigenvalues and eigenvectors of a square matrix, degenerate eigenvalues, diagonalisation of a square matrix, application to coupled systems of ordinary differential equations with examples from mechanics and ecology. MATLAB exercises.

Module 2: Linear Algebra (Abstract)

Definition and basic properties of abstract vector spaces; examples; Inner products; Cauchy-Schwarz inequality; Subspaces; Definition of dimension; Finite vector spaces and bases; The isomorphism theorem; Linear Transformations. Basic definitions: rank, null space, etc. The fundamental theorem; Special transformations: projections, orthogonal transformation, symmetric transformations, stochastic matrices; Spectral theorem for symmetric matrices; Matrix functions: matrix exponential, power series.

Textbook(s)

Nil

Prerequisite(s)

Students need to have passed SACE Stage 2 Mathematical Methods or equivalent.

Corequisite(s)

Nil

Teaching method

Component	Duration
INTERNAL, MAWSON LAKES
Seminar	2 hours x 13 weeks
Seminar	2 hours x 13 weeks
Tutorial	1 hour x 12 weeks
Computer Practical	1 hour x 12 weeks

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Assessment

Examination, Problem solving exercise, Test/Quiz

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 1)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
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Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the university. To determine the cost of this course, go to:
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Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.