Eigen value - Definition: Let n n A be a matrix. If there...

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Unformatted text preview: Definition: Let n n A be a matrix. If there exists a nonzero vector n R x such that x x = A , then real no. is called an eigenvalue of A and every x is called an eigenvector of A associated with . Eigenvalues are also called proper values, characteristic values and latent values ; and eigenvectors are also called proper vectors, characteristic vectors and latent vectors . Remarks : 1. 0 cannot be an eigenvector but 0 can be an eigenvalue. 2. A may have many different eigenvectors associated with an eigenvalue , since , r r x is also an eigenvector if x is an eigenvector of A . Ex.1 : Let n I A = . Find its eigenvalues and corresponding eigenvectors. Sol. : Eigenvalue : 1 = Eigenvector : every nonzero vector n R x Ex.2 : Let = 2 6 1 3 A Find the eigenvalues of A and associated eigenvectors. Sol. : Eigenvalue : 5 , = Eigenvectors associated with = : , 3 - r r r , In particular,...
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This note was uploaded on 05/14/2010 for the course MATHEMATIC mathe taught by Professor Xyz during the Spring '10 term at Birla Institute of Technology & Science.

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Eigen value - Definition: Let n n A be a matrix. If there...

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