This module builds on the material covered in the MATH1804. It introduces the student to the concepts of vector spaces; and eigenvalues and eigenvectors.
Vector Spaces
Introduction and definition of vector spaces. Examples of vector spaces. Euclidean n-space. Subspaces. Linear combinations of vectors. Spanning and linearly independent sets. Bases. Dimension of a vector space. Row and column space of a matrix. Rank of a matrix. Complex vector spaces.
Inner Products
Inner product spaces. Orthogonality. Change of basis. Orthogonal matrices. Least squares problems.
Linear Transformations
Linear transformations and their matrices. Kernel and range. Similarity.
Eigenvalues and Eigenvectors
Eigenvalues and eigenvectors. Eigenspace of a matrix. Diagonalization of a matrix. Complex eigenvalues. Applications to systems of differential equations.
Lectures supported by tutorials
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |