Module: Linear Mathematics II

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Linear Mathematics II
Module Code	MTH1011 (ITS: MS104)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

The purpose of this module is to introduce to students who have successfully completed Linear Mathematics 1 further foundational topics in Linear Algebra. The emphasis is on students gaining a sound knowledge of basics and fundamental computational skills. Eigenvalues and eigenvectors are important in calculus of several variables, probability and statistics. The course is delivered through a combination of lectures, and tutorials facilitated by a tutor.

Learning Outcomes

1. demonstrate computational skills by solving wide range of drill problems related to the indicative syllabus
2. state selected definitions and theorems related to the indicative syllabus
3. solve exercises that test understanding of these definitions and theorems
4. explain arguments used to prove selected theorems in special cases

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Lectures
Tutorial	11	Tutorial and examples class
Independent Study	44	Solving exercises on tutorial sheets
Independent Study	22	Preparation for class tests and final exam
Independent Study	24	Assimilating lecture material
Total Workload: 125

Section Breakdown
CRN	20779	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	James O'Shea

Type	Description	% of total	Assessment Date
Assessment Breakdown
Assignment	Homework assignments and/or in-class tests	20%	As required
Formal Examination	End-of-Semester Final Examination	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
Spaces of real and complex vectors; linear mappings; subspaces; linear independence; basis and dimension; row space, column space and null space; rank and nullity

Inner product spaces
standard inner products; Cauchy-Schwarz inequality; angle and orthogonality; orthonormal bases and Gram-Schmidt procedure; orthogonal matrices; positive and negative definite matrices; least squares approximation; least square solutions; orthogonal projections

Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors; diagonalisation; Diagonalisation of symmetric and Hermitian matrices

Indicative Reading List

Books:

H. Anton and C. Rorres: 2005, Elementary Linear Algebra - Applications Version, 9th or 10th, John Wiley & Sons, Inc.,

Articles:
None

Other Resources

None