MATH20300 Linear Algebra 2 for the Mathematical Sciences

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
Lectures

23

Tutorial

12

Autonomous Student Learning

51

Online Learning

24

Total

110

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
Pre-requisite:
MATH10340 - Linear Algebra 1 (MPS)

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

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade

Not yet recorded.

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour