Question: Suppose that and are two different eigenvalues of the square matrix A. Prove that the intersection of the eigenspaces for these two eigenvalues

Suppose that λ and ρ are two different eigenvalues of the square matrix A. Prove that the intersection of the eigenspaces for these two eigenvalues is trivial. That is, εA (λ) ∩ εA (ρ) = {0}.

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