This module builds on the material covered in a first year Linear Algebra module. It introduces the learner to the concepts of vector spaces, linear transformations and eigenvalues and eigenvectors.
Review
Linear systems, matrix algebra, determinants including use of mathematical software
Vectors & Vector Spaces
Vectors in n-space, norm of a vector, Euclidean inner product, orthogonality, general vector spaces, subspaces, linear combination of vectors, linear dependence, spanning sets, basis, dimension of a vector space.
Linear Transformations
Standard matrix for a linear transformation, reflections, rotations and projection operators, row and column space of a matrix, rank and nullity of a matrix, The Rank Nullity Theorem.
Eigenvalues and Eigenvectors
Characteristic equation of a matrix, eigenvalues and eigenvectors of a matrix, eigenspace of a matrix, diagonalization of a matrix.
Lectures supported by tutorials and laboratory sessions
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |