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.
Curricular information is subject to change.
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.
[Disclaimer: module content and assessment strategies may be subject to minor changes during the trimester. These changes may not be reflected in this module descriptor at that time, but will be clearly communicated to all students via other means.]
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.
[Disclaimer: module content and assessment strategies may be subject to minor changes during the trimester. These changes may not be reflected in this module descriptor at that time, but will be clearly communicated to all students via other means.]
About this Module
The United Nations identified seventeen Sustainable Development Goals (SDGs) as core to the 2030 Agenda for Sustainable Development, and UCD contributes in general to SDG 4 Quality Education. Further SDGs explored within this module if relevant are listed below. A scale of 1 - 5 indicates the extent to which the SDG is covered.
Student Effort Hours:
| Student Effort Type | Hours |
|---|---|
| Lectures | 30 |
| Tutorial | 6 |
| Specified Learning Activities | 30 |
| Autonomous Student Learning | 50 |
| Total | 116 |
Approaches to Teaching and Learning:
The intention is to have most contact hours face-to-face.Some of the lectures may be in blended or on-line format.
Requirements, Exclusions and Recommendations
Not applicable to this module.
Module Requisites and Incompatibles
Not applicable to this module.| Resit In | Terminal Exam |
|---|---|
| Spring | Yes - 2 Hour |
Not yet recorded