Building on the intuitive understanding and calculation techniques from Linear Algebra I, this module introduces the concepts of vector spaces and linear maps in an abstract, axiomatic way. In particular, matrices are revisited as the representation of a linear map in a specific basis. We furthermore introduce the concept of bases of vector spaces and study diagonalisation of linear maps.
We apply the abstract theory both in the context of Rn (as seen in Linear Algebra I) and in the context of function spaces; these are particularly important in the study of linear differential equations and hence for instance in physical sciences; for example we look at the derivative operator on the space of polynomial functions.
One of the pre-requisites for MATH2003, MATH2014, MATH2045, MATH3033, MATH3076 and MATH3090
Prerequisites: (MATH1006 OR MATH1008 OR MATH1059) AND MATH1048