Semester I

This module deals with vector spaces and linear transformations. Matrix algebra is also described in detail with real entries, and techniques for their manipulation and solution methods of systems of linear equations, the module contains eigenvalues, eigenvectors, and diagonalization. Finally, it covers Affine coordinates; straight lines in affine space; Segments; Inner product, length, orthogonality in inner product spaces, orthogonal bases, Gram Schmidt Orthogonalization, Direct Sum, Orthogonal complement, Least Square.