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[marek-knows.com]

I have a symetric 3x3 matrix in C++. I need to find the eigenvalues and eigenvectors of this matrix in an optimal fashion. Can anyone point me to some pseudocode on how to do this? I can do it by hand on a piece of paper, but I'm sure there is a more optimal technique to calculate the vectors and values when using a computer.

[Reedbeta]

This page outlines a method for finding the eigenvalues of a 3x3 matrix by numerically solving the characteristic polynomial, and suggests a few different heuristic approaches for getting eigenvectors. This Wikipedia article talks more about numerical computation of the null space of a matrix (the eigenvectors of A are bases of the null space of A - lambda*I for each eigenvalue lambda). QR decomposition is probably the easiest-to-code approach and probably works fine for a 3x3 matrix. The article also talks about singular-value decomposition (SVD), which is a more complicated but more numerically stable technique.