eigenvalue - Eigen Values Eigen Vectors Let A be n x n...

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Eigen Values & Eigen Vectors
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Let A be n x n matrix. is eigen value of A if there exists a nonzero vector n R x such that x Ax x is called an eigen vector of A associated with
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Eigen value / proper value / characteristic value / latent value eigen vector / proper vector / characteristic vector / latent vector .
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NOTE: 0 can not be an eigenvector but 0 can be an eigenvalue. A may have many different eigenvectors associated with an eigenvalue , since 0 r , rx is also an eigenvector if x is an eigenvector of A .
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Ex.1 : Let n I A . Find it’s eigenvalues and corresponding eigenvectors. Sol. : Eigenvalue : 1 Eigenvector : every nonzero vector n R x
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Ex.2 : Let 2 6 1 3 A Find the eigenvalues of A and associated eigenvectors.
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Sol. : Eigenvalue : 5 , 0 Eigenvectors associated with 0 : 0 , 3 r r r , In particular, 3 1 Eigenvectors associated with 5 : 0 , 2 r r r , In particular, 2 1
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Definition : Let ] [ ij n n a A . Then nn n n n n n a a a a a a a a a A I f
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