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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 = λ v for some scalar λ , which is then called an eigenvalue of A . The vector v is called an eigenvector corresponding to the eigenvalue λ . 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 λ = 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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This note was uploaded on 04/15/2008 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas.
 Spring '08
 PAVLOVIC
 Linear Algebra, Algebra, Eigenvectors, Vectors

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