# MATH220, Linear Algebra II

Undergraduate course, *Lancaster University, Department of Mathematics & Statistics*, 2017

My role: Graduate Teaching Assistant

Main topics:

Vector spaces over a field (with emphasis on Rn): subspaces, spanning, linear independence, bases, dimension.

Linear transformations (with emphasis on geometrical examples): invertibility, matrices of linear transformations, kernel and image, rank of a matrix, applications to linear equations.

Change of basis: eigenvectors and eigenvalues, characteristic equation, diagonalisation of square matrices.

Euclidean spaces: orthonormal bases, orthogonal matrices, orthogonal diagonalisation of a real symmetric matrix.

Jordan Normal Form.