My role: Graduate Teaching Assistant
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.