Module: Linear Algebra

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-ordinator	Semester 1: Ronan Egan Semester 2: Ronan Egan Autumn: Ronan Egan
Module Teachers	Ronan Egan
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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; 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

None

Programme or List of Programmes

ACM	BSc in Actuarial Mathematics
AFU	Age Friendly University Programme
BPM	BSc in Psychology with Mathematics
BSSA	Study Abroad (DCU Business School)
BSSAO	Study Abroad (DCU Business School)
CAFM	Common Entry, Actuarial, Financial Maths
HMSA	Study Abroad (Humanities & Soc Science)
HMSAO	Study Abroad (Humanities & Soc Science)
IESA	Study Abroad (Institute of Education)
IESAO	Study Abroad (Institute of Education)
SHSA	Study Abroad (Science & Health)
SHSAO	Study Abroad (Science & Health)

Date of Last Revision

28-JAN-10

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