Many difficult problems can be handled easily once relevant information is organized in a certain way. This subject aims to teach students how to organize information (in cases where certain mathematical structures are present) about vector spaces in a way that makes problems involving linear functions of many variables easier (or at least tractable) to analyse and solve.

On completion of this subject students should be able to define Euclidean space and its subspaces, define vector spaces, perform linear transformation, calculate inner product, show orthogonally and orthonormal vectors, use technique for decomposing a matrix (Gram-Schmidt Process and QR-Decomposition), calculate best approximate solution, fit models to data and analyze the accuracy of the fit, carry out function approximation.