Module: Linear Algebra

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Linear Algebra
Module Code	MS217 (ITS) / MTH1039 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Ronan Egan
Module Teachers	Niamh O'Sullivan
NFQ level	8	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination
Array

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.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	20	Lecture
Tutorial	10	tutorial
Independent Study	95	No Description
Total Workload: 125

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	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	Class test	10%	Week 7
Loop Quiz	n/a	10%	As required

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

Sheldon Axler: 2004, Linear Algebra done right, 7th Ed., Springer,
T.S. Blyth, E. F. Robertson: 2001, Further Linear Algebra, Springer,
P.R. Halmos: 1993, Finite Dimensional Vector Spaces, 5th Ed., Springer,

Other Resources

None