In this chapter we describe numerical techniques for the calculation of a scalar λ and non-zero vector x in the equation $$ Ax = \lambda x $$ (4.1) where A is a given n × n matrix. The quantities λ and x are usually referred to as an eigenvalue and an eigenvector of A. They arise in many different branches of mathematics including quadratic forms, differential systems and non-linear optimization, and can be used to solve problems from such diverse fields as economics, information theory, structural analysis, electronics and control theory.