Lecture 5
Further examples of Jordan form. Discussion and illustration of the sensitivity of Jordan form to perturbations. Applications of Jordan form: (i) calculating matrix inverses, (ii) determining powers of a matrix in Jordan form, (iii) exponentiation of a matrix in Jordan form.
Lecture 6
Matrix norms, common examples. Condition number: definition and interpretation.
Lecture 7 and 8
Cayley-Hamilton Theorem. Examples and a proof (using Jordan form).