Syllabus
- An abstract definition and examples of vector spaces
- Subspaces, spans and related results
- Linearly dependent and linearly independent sets and related results
- Bases, dimension and related results
- Linear mappings, the image and the kernel, and related results
- Coordinates of vectors, matrices of linear mappings, change of basis
- The concept of the rank of a matrix and of a linear mapping
On completion of the course students should be able to:
- Read and understand advanced abstract mathematical definitions in textbooks and other sources
- Prove simple properties of linear spaces from axioms
- Check whether a set of vectors is a basis
- Check whether a mapping is a linear mapping
- Check whether a linear mapping is onto and whether it is one-to-one
- Find a matrix of a linear mapping
- Change a basis and recalculate the coordinates of vectors and the matrices of mappings