## Diagonalizable & Minimal Polynomial

A matrix or linear map is diagonalizable over the field if and only if its minimal polynomial is a product of distinct linear factors over .

## Characteristic Polynomial

Let be an matrix. The characteristic polynomial of , denoted by , is the polynomial defined by

## Cayley-Hamilton Theorem

Every square matrix over a commutative ring satisfies its own characteristic equation:

If is an matrix, where .