Lecture Slides 13

# Lecture Slides 13 - AMS 210: Applied Linear Algebra October...

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AMS 210: Applied Linear Algebra October 20, 2009 AMS 210

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Topics Today Problem Set 7 Eigenvalue/Eigenvector Matrix Decomposition Eigenvector Matrix-based Analysis of Growth Models A Theorem On Eigenvalues/Eigenvectors Solving a System of Equestions by Iteration Jacobi Iteration AMS 210
Problem Set 7 This week’s problem set is due next Thursday, October 29. Read section 3.3. Exercises: 3.3: 2cd, 4a, 5a, 7a, 9a, 15, 33i, 34i. Show work. If multiple sheets, stapling is strongly preferred. Graders might deduct points for insecurely bound/collated problem sets. AMS 210

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Eigenvalue/Eigenvector Matrix Decomposition In matrix notation: 1 Use e.g. Gaussian elimination and/or inverses to ﬁnd x as linear combination of eigenvectors. Get c = U - 1 x . 2 Use ± a λ k 1 b λ k 2 ² = ± λ k 1 0 0 λ k 2 ²± a b ² = ± λ 1 0 0 λ 2 ² k ± a b ² or c 0 = D k λ c where D λ is diagonal matrix of eigenvalues, to write corresponding part of previous expression. 3 Express as linear combination of eigenvalues A k x = a λ k 1 ± u 1 u 2 ² + b λ k 2 ± v 1 v 2 ² = U ± a λ k 1 b λ k 2 ² = Uc 0 where U is the matrix with eigenvectors as columns. Then
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## This note was uploaded on 12/06/2011 for the course AMS 211 taught by Professor Shuaixue during the Fall '09 term at SUNY Stony Brook.

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Lecture Slides 13 - AMS 210: Applied Linear Algebra October...

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