Transcription of Eigenvalues and Eigenvectors
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5 2012 Pearson Education, Inc. Eigenvalues and Eigenvectors Eigenvectors AND Eigenvalues Slide 2 2012 Pearson Education, Inc. Eigenvectors AND Eigenvalues Definition: An eigenvector of an matrix A is a nonzero vector x such that for some scalar . A scalar is called an eigenvalue of A if there is a nontrivial solution x of ; such an x is called an eigenvector corresponding to . is an eigenvalue of an matrix A if and only if the equation ----(1) has a nontrivial solution. The set of all solutions of (1) is just the null space of the matrix . nn x xA=x xA=( )x0AI =nn AI Slide 3 2012 Pearson Education, Inc. Eigenvectors AND Eigenvalues So this set is a subspace of and is called the eigenspace of A corresponding to.
© 2012 Pearson Education, Inc. Slide 5.1- 10 EIGENVECTORS AND EIGENVALUES ! The scalar λ is an eigenvalue of A if and only if the equation has a nontrivial solution,
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