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.