Module: Linear Algebra II

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Linear Algebra II
Module Code	MTH1089
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	7.5

Description

The purpose of this module is to introduce to students who have successfully completed Linear Algebra I. The emphasis is on students gaining a sound knowledge of eigenvalues and eigenvectors of abstract vector spaces, Singular Value Decomposition, and Jordan Canonical Form.

Learning Outcomes

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	No Description
Tutorial	12	No Description
Independent Study	170	No Description
Total Workload: 218

Section Breakdown
CRN	21139	Part of Term	Semester 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

Type	Description	% of total	Assessment Date
Assessment Breakdown
Written Exam	In class tests	20%	n/a
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

Determinants
Determinants of square matrices, ways to calculate them, their geometric meaning, their relationship to eigenvalues.

Eigenvalues and eigenvectors
Definitions of eigenvalues and eigenvectors, understanding what they represent in the context of a linear transformation, applications.

Matrix decomposition
Diagonalisation, singular value decomposition, Jordan canonical form

General vector spaces
Vector spaces over fields other than the reals, examples of different vector spaces e.g., function spaces, inner products, orthogonality, projection.

Indicative Reading List

Books:

Gilbert Strang: 2023, Introduction to Linear Algebra, Wellesley-Cambridge Press, 0, 1733146679
Sheldon Axler: 2023, Linear Algebra Done Right, Springer, 0, 3031410254

Articles:
None

Other Resources

None