eig_2009_09_28_02_2up

eig_2009_09_28_02_2up - 5 - 1 Eigenvectors S. Lall,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 5

eig_2009_09_28_02_2up - 5 - 1 Eigenvectors S. Lall,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online