Slides_2010_03_10

# Slides_2010_03_10 - Applied linear algebra and numerical...

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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 take-home 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 take-home turned after 17:00 (03/15/10) will be considered late and not graded. Eigenvalue and Eigenvectors Consider a non-zero matrix A ∈ R n × n . Definition The vector v 6 = is an eigenvector of A if Av = λ v for some scalar value λ . The scalar λ is called an eigenvalue . How to find eigenvalues? Consider a non-zero matrix A ∈ R n × n . • If λ is an eigenvalue of A , then A- λ I is a singular matrix. • N ( A- λ I ) 6 = { } • det ( A- λ I ) = • Eigenvalues are the roots for the characteristic polynomial λ 7→ det ( A- λ I ) (of degree n ). • There are at most n eigenvalues. How to find eigenvalues? • Eigenvalues are the roots for the characteristic polynomial λ 7→ det ( A- λ I ) (of degree n ). Definition The algebraic multiplicity for an eigenvalue λ is the multiplicity of λ as a root of the characteristic polynomial....
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Slides_2010_03_10 - Applied linear algebra and numerical...

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