Power Method

Let . An eigenvalue of is called a dominant eigenvalue if has Algebraic Multiplicity of and for all other eigenvalues .

Power method is a useful method to find the dominant eigenvalue. The idea is to use the property of the diagonalization such that where .

Power method picks a random . Then iterates for :

Where we use the Infinity Norm. After many iterations we are left with the following result:

We can then find the eigenvalue using .