The Cayley Hamilton Theorem

The Cayley-Hamilton theorem states that a square matrix satisfies its own characteristic polynomial. In this lecture we try to make sense of this statement, and discuss how this result can be used to 'simplify' infinite sums and find matrix inverses.

The Cayley Hamilton theorem can be proved using properties of the adjugate matrix. We briefly go through the steps

A rather brief written version of this proof can be found here.