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Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

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Module Title
Module Code (ITS)
Faculty School
Module Co-ordinatorSemester 1: Ronan Egan
Semester 2: Ronan Egan
Autumn: Ronan Egan
Module TeachersRonan Egan
NFQ level 8 Credit Rating
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.



Workload Full-time hours per semester
Type Hours Description
Lecture20Lecture
Tutorial10tutorial
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.

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% Examination Weight%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class TestClass test10%Week 7
Loop Quizn/a10%As required
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

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