Aims

The aims of the course are to:

• Introduce the ideas and techniques of Linear Algebra, and illustrate some of their applications in engineering.

Objectives

As specific objectives, by the end of the course students should be able to:

• For all objectives, complete calculations by hand for small problems, or by using Matlab for larger problems (the IB Computing Course deals with this in detail).
• Solve a set of linear equations using Gaussian elimination, and complete the LU factorisation of a matrix.
• Understand, and be able to calculate bases for the four fundamental subspaces of a matrix.
• Calculate the least squares solution of a set of linear equations.
• Orthogonalize a set of vectors, complete the QR factorisation of a matrix, and be able to use this to find the least squares solution of a set of linear equations.
• Find the eigenvalues and eigenvectors of a matrix, and complete the A = SL S-1 or A = QL QT factorisations as appropriate.
• Find the SVD of a matrix, and to understand how this can be used to calculate the rank of the matrix, and to provide a basis for the each of its fundamental subspaces.

Content

• Solution of the matrix equation Ax = b: Gaussian elimination, LU factorization, the four fundamental subspaces of a matrix.
• Least squares solution of Ax = b for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
• Solution of Ax = l x, eigenvectors and eigenvalues.
• Singular Value Decomposition (if time)

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 17/05/2018 15:36