> Solving the resulting equation is one way of computing eigenvalues. But it might not be the one you want to use in some practical situation. Related fun fact

> Solving the resulting equation is one way of computing eigenvalues. But it might not be the one you want to use in some practical situation. Related fun fact: Solving the eigenvalue equation is (in general) impossible in closed form for matrices 5x5 or larger, because there's no closed form solution to the quintic. So some other algorithm for finding eigenvectors and eigenvalues is often absolutely required in practice.