Cayley-Hamilton Theorem

Cayley-Hamilton Theorem

## Definition / Concept

Every square matrix satisfies its own characteristic equation.

For a $$2\times2$$ matrix:

$$A^2-(\operatorname{tr}A)A+|A|I=O$$

where $$\operatorname{tr}A$$ is the trace of $$a$$.

## Usage

- Used to reduce higher powers of a matrix to lower powers.