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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Linear Algebra
Module Code MS217
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Ronan Egan
Semester 2: Ronan Egan
Autumn: Ronan Egan
Module TeachersRonan Egan
NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Repeat examination

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
Independent Study95No 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.

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 Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class TestClass test10%Week 7
Loop Quizn/a10%As required
Reassessment Requirement Type
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 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

Programme or List of Programmes
ACMBSc in Actuarial Mathematics
AFUAge Friendly University Programme
BPMBSc in Psychology with Mathematics
BSSAStudy Abroad (DCU Business School)
BSSAOStudy Abroad (DCU Business School)
CAFMCommon Entry, Actuarial, Financial Maths
HMSAStudy Abroad (Humanities & Soc Science)
HMSAOStudy Abroad (Humanities & Soc Science)
IESAStudy Abroad (Institute of Education)
IESAOStudy Abroad (Institute of Education)
SHSAStudy Abroad (Science & Health)
SHSAOStudy Abroad (Science & Health)
Date of Last Revision28-JAN-10

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