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Finding the Eigenvalues and Eigenvectors of a Symmetric Real Matrix

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
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A symmetric real matrix admits only real eigenvalues. We show how one can find these eigenvalues as well as their corresponding eigenvectors without using Mathematica's built-in commands (Eigenvalues and Eigenvectors). This iterative technique is described in great details in the book by Kenneth J. Beers, Numerical Methods for Chemical Engineering, Applications in Matlab, Cambridge University Press, 2007. It allows the determination of the largest and the smallest eigenvalues as well as any eigenvalue nearest to some target value.

*Applied Mathematics
*Applied Mathematics > Numerical Methods
*Engineering > Chemical Engineering
*Science > Chemistry

Eigenvalues, Eigenvectors, iterative technique, symmetric matrix
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Extremal_Eigenvalues.nb (118.5 KB) - Mathematica Notebook [for Mathematica 5.2]