Module: Linear Algebra

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Linear Algebra
Module Code	MTH1039 (ITS: MS217)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

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

Section Breakdown
CRN	12312	Part of Term	Semester 1 & 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Ronan Egan	Module Teacher	Niamh O'Sullivan

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	Class test	20%	Week 7
Formal Examination	n/a	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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.

Indicative Reading List

Books:

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,

Articles:
None

Other Resources

None