申論題

6. (15pts) Let V be a fnite dimensional vector space over C. Let T : V →Vbe a linear map and

let W be an T-invariant subspace of V. Suppose that U₁, U₂, , U_n are eigenvectors in V of T

corresponding to distinct eigenvalues λ₁,  λ₂, , λ_n in C. Prove that if u₁ +u₂+...+

then. (Hint: induction on n)