Advanced Math proof? Theorem 7.3. Let T be a linear operator on a finite-dimensional vector space V with distinct eigenvalues A1, A2,..., A. For each i=1,2,..., k, let S, be a linearly independent subset of K. Then S, S, = Ø for ij, and S=S₁ US₂U.. US is a linearly independent subset of V.

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