MATH20300 Linear Algebra 2 for the Mathematical Sciences

Academic Year 2023/2024

This is a second university course in Linear Algebra, delving deeper into the concepts and applications of this beautiful subject.
The successful student will gain a solid understanding of the theoretical aspects of linear algebra as well as the ability to carry out practical computations, and the ability to apply concepts and techniques to unseen problems.

The topics discussed will include:
Vector spaces over a field - axiomatic definition, span, linear independence, bases, dimension, sum, direct sum;
Linear maps - definition, rank-nullity, matrix of a linear map, change of basis, column and row rank;
Eigen theory - eigenvalues, eigenvectors, eigenspaces and diagonalization of linear maps;
Inner products - Gram-Schmidt, orthogonal endomorphisms. (TIME PERMITTING)

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Curricular information is subject to change

Learning Outcomes:

Upon successful achievement of the learning outcomes the student will be able to:

Prove elementary facts and identities related to the axioms of a vector space.
State and unpack the fundamental definitions of linear algebra.
State and prove the key theorems in the subject.
Determine whether or not given sets of vectors form a vector subspace.
Compute the span of a set of vectors.
Decide if a set of vectors are linearly independent or not.
Calculate the basis and dimension of a vector space.
Apply the Rank-Nullity theorem.
Find the image and nullspace of a linear transformation along with their bases.
Calculate the change of basis matrix.
Calculate the characteristic polynomial, eigenvalues, eigenvectors, and eigenspaces of a linear transformation.
Determine when a linear transformation is diagonalzable and when it is not.
Prove facts about inner product spaces.
Apply known results to unseen problems and applications.

Student Effort Hours: 
Student Effort Type Hours
Autonomous Student Learning






Online Learning




Approaches to Teaching and Learning:
A significant portion of this module will be delivered and assessed online via Brightspace. I won't ask you to purchase any textbooks for this course but it might be helpful to have a copy of "Linear Algebra" by Serge Lang (ISBN: 978-1-4757-1949-9). 
Requirements, Exclusions and Recommendations
Learning Requirements:

A good first year knowledge of undergraduate linear algebra will be assumed, such as that given in MATH10340, or its equivalent from other universities.

Module Requisites and Incompatibles
MATH10340 - Linear Algebra 1 (MPS)

MATH20030 - Linear Algebra 2 (Sci)., MST20050 - Linear Algebra II

Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: 5 Homework assignments spread across the term. No remediation. Varies over the Trimester n/a Graded No


Examination: Final examination held at the end of the trimester 2 hour End of Trimester Exam No Graded No


Examination: Mid-trimester exam to be held halfway through the course. No remediation.
Week 7 No Graded No



Carry forward of passed components
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, on an activity or draft prior to summative assessment
• Group/class feedback, post-assessment
• Peer review activities
• Self-assessment activities

How will my Feedback be Delivered?

An important part of this module is self-directed learning and knowing when a submission is good enough to meet the module's learning outcomes. Therefore you will have opportunities to review your peers' work as well as having your own work reviewed by your peers BEFORE submission.

Name Role
Andrew Mullins Tutor