JC1005: LINEAR ALGEBRA (2022-2023)

Last modified: 31 Jul 2023 11:19

Course Overview

Linear algebra is the study of linear equations and matrices. At a more abstract level, it concerns vector spaces and linear maps between them, and it is a central subject within mathematics. It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others.

Course Details

Study Type	Undergraduate	Level	1
Term	First Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	Offshore	Sustained Study	No
Co-ordinators	Sorry, we don't have a record of any course coordinators.

What courses & programmes must have been taken before this course?

Any Undergraduate Programme (Studied)

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

Course Description

This course is an introduction to linear algebra over the real numbers and the complex numbers. It covers linear equations and matrices, vector spaces and linear maps, and eigenvectors and eigenvalues.

Syllabus

Solving a linear system. Elementary row operations, row echelon form, Gaussian algorithm for solving a linear system.
Vector spaces. Definition of a vector space over the real and complex numbers. Subspaces of a vector space, intersection and sum of subspaces. Span, spanning sets. Linear independence. Basis, dimension. Elementary results about bases and dimension. Change of basis matrix. The algebra of nxn-matrices.
Linear maps. Definition of a linear map between vector spaces. Kernel, image, injective, surjective linear maps. Matrix of a linear map. Rank of a matrix. Invertible matrices. Change of basis and the matrix of a linear map.
Determinants of matrices and linear transformations.
The various definitions of the determinant. Properties and methods of calculation. Finding the inverse of a matrix using cofactors.
Determinants of matrices and linear transformations.
Eigenvalues and eigenvectors of square matrices and of endomorphisms. Properties.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

There are no assessments for this course.

Formative Assessment