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Unformatted text preview: 5 - 1 Eigenvectors S. Lall, Stanford 2009.09.28.02 5. Eigenvectors Eigenvectors and eigenvalues Properties Scaling interpretations Diagonalization 5 - 2 Eigenvectors S. Lall, Stanford 2009.09.28.02 Eigenvectors and eigenvalues C is an eigenvalue of A C n n if X ( ) = det( I A ) = 0 equivalent to: there exists nonzero v C n s.t. ( I A ) v = 0 , i.e. , Av = v any such v is called an eigenvector of A (associated with eigenvalue ) there exists nonzero w C n s.t. w T ( I A ) = 0 , i.e. , w T A = w T any such w is called a left eigenvector of A 5 - 3 Eigenvectors S. Lall, Stanford 2009.09.28.02 Properties if v is an eigenvector of A with eigenvalue , then so is v , for any C , 6 = 0 even when A is real, eigenvalue and eigenvector v can be complex when A and are real, we can always find a real eigenvector v associated with : if Av = v , with A R n n , R , and v C n...
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- Fall '08