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Unformatted text preview: ? IMPORTANT DEFINITIONS. An eigenvector for a p p matrix A is a nonzero vector v such that A v = v for some scalar , which is then called an eigenvalue of A . The vector v is called an eigenvector corresponding to the eigenvalue . EXAMPLE. Calculate the following and draw some conclusions and make some guesses. 2 1 31 5 0 0 4 5 1 2 1 31 5 0 0 13 FACT. The eigenvalues of a triangular matrix are the entries on its diagonal. FACT. Eigenvectors that correspond to distinct eigenvalues are linearly independent. WHY? EXAMPLE. Find a basis for the eigenspace corresponding to the eigenvalue = 4 for the matrix A = 3 0 2 0 1 3 1 0 0 1 1 0 0 0 0 4 . HOMEWORK: SECTION 5.1...
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 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra, Eigenvectors, Vectors

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