Abstract
Suppose A is an n × n matrix with real elements, and that λ = λ1 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 λ1,(b)matrix is defective, and we have only one linearly independent eigenvectors corresponding to the double root λ1.
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