Change of basis matrices. Composition of linear maps and their matrices. Matrices of f with respect to different bases are similar. Diagonalisability of matrices and eigenvalues Diagonal matrices. Eigenvalues and eigenvectors.
Similar matrices have the same characteristic polynomial.
Finding eigenvectors by solving systems of linear equations. Determinant and trace in terms of eigenvalues. Conditions for diagonalisability. Algebraic and geometric multiplicity of eigenvalues. Real symmetric and hermitian matrices.