Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Linear Algebra
Module Code	MS217
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Thomas Brady Semester 2: Thomas Brady Autumn: Thomas Brady
Module Teacher	Thomas Brady
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module is a second course in linear algebra. In this module students will consider abstract vector spaces and linear transformations and will study the various canonical forms for matrices.The participants are expected to have a proficiency with geometric vectors and matrices. This module provides the linear algebra tools for for such courses as vector calculus and probability.Students are expected to attend lectures, participate in tutorials and take in-class tests.

Learning Outcomes

1. Give selected definitions and prove selected theorems
2. Demonstrate an understanding of the mechanics of change of basis.
3. Compute canonical forms for matrices.
4. Apply the spectral theorem for real symmetric matrices.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	36	Lecture
Tutorial	12	tutorial
Independent learning time	140	No Description
Total Workload: 188

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Vector spaces.
Abstract vector spaces and linear transformations. Rank-nullity theorem.

Matrix representations.
Coordinates, matrix representations, similarity..

Projection.
Inner products, orthogonal vectors, projection, least squares..

Complex matrices..
Complex vector spaces and matrices, complex inner product, unitary similarity, spectral theorem..

Jordan canonical form.
Hamilton-Cayley theorem, primary decomposition, Jordan bases, Jordan forms..

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Short answer questions	In-class tests	25%	Every Second Week

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 1

Indicative Reading List