MATH30030 Advanced Linear Algebra

Academic Year 2023/2024

In this module we introduce and develop some of the more advanced ideas in Linear Algebra. A sample of topics covered are:

Inner product spaces, bilinear forms, dual spaces, transpose and adjoint, Gram-Schmidt process. Quotient spaces. Multilinear algebra, tensor products of vector spaces, symmetric and alternating group, determinants. Endomorphisms, minimal polynomials, Cayley-Hamilton theorem. Invariant subspaces. Companion matrices, Vandermonde matrices, circulant matrices.

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Curricular information is subject to change

Learning Outcomes:

On completion of this module, the student is expected to:- demonstrate an understanding of the theoretical aspects covered in this module;- be able to carry out any computations involving the objects described in this module.

Student Effort Hours: 
Student Effort Type Hours




Specified Learning Activities


Autonomous Student Learning




Approaches to Teaching and Learning:
Problem-based learning via lectures, tutorials, a midterm and a final exam. 
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
Not applicable to this module.
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Class Test: Class tests/Homework (2 x 20% each) Unspecified n/a Alternative linear conversion grade scale 40% No


Examination: Final Exam 2 hour End of Trimester Exam No Alternative linear conversion grade scale 40% 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

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.