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Unformatted text preview: Applied linear algebra and numerical analysis Session 27 Prof. Ulrich Hetmaniuk Department of Applied Mathematics March 11, 2010 Take Home Exam The takehome for AMATH 352 has two deadlines. The Scorelator part is due before 12:30 on 03/15/2010. The written part is due on 03/15/2010 before 17:00. To turn the written part, you can either give it to me on Friday; put it in the mailbox next to the elevator on the 4th floor of Guggenheim; give it to Xing Fu between 16:30 and 17:00 on Monday March 15th, 2010 (GUG 415). Any takehome turned after 17:00 (03/15/10) will be considered late and not graded. Eigenvalue and Eigenvectors Consider a nonzero matrix A R n n . Definition The vector v 6 = is an eigenvector of A if Av = v for some scalar value . The scalar is called an eigenvalue . How to find eigenvalues? Consider a nonzero matrix A R n n . If is an eigenvalue of A , then A I is a singular matrix. N ( A I ) 6 = { } det ( A I ) = Eigenvalues are the roots for the characteristic polynomial 7 det ( A I ) (of degree n ). There are at most n eigenvalues. How to find eigenvalues? Eigenvalues are the roots for the characteristic polynomial 7 det ( A I ) (of degree n ). Definition The algebraic multiplicity for an eigenvalue is the multiplicity of as a root of the characteristic polynomial....
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 Winter '07
 Leveque
 Numerical Analysis

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