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)

HIll, Richard O. 1996, Elementary Linear Algebra with Applications, 3rd edition

Kleinfeld, E., & Kleinfeld, M. 2001, Understanding Linear Algebra Using MATLAB, -, Prentice Hall, -

Prerequisite(s)

Corequisite(s)

Nil

Teaching method

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

Assessment

Assignment, Continuous assessment, Examination

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
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Fee-paying program for domestic and international students
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* 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.