The Simple Iterative Method Applied to a Matrix Which has a Dominant Double Real Eigenvalue

Suppose A is an n × n matrix with real elements, and that λ = λ 1 is a dominant double real eigenvalue. We will assume for simplicity that none of the order eigenvalues are repeated. Then there are two possibilities ( a ) matrix is non-defective, and we can find two linearly independent eigenvectors corresponding to the double root λ 1 , ( b ) matrix is defective, and we have only one linearly independent eigenvectors corresponding to the double root λ 1 .