# Soliving 3x3 generalized eigenvectors

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Hi All, I'm looking for a simple as possible algorithm/sourcecode, for finding the generalized eigenvectors of a 3x3 matrix, namely: Av = lambda Bv (http://en.wikipedia.org/wiki/Generalized_eigenvector , the second item in the "Other meanings of the term" section). Thanks in advance, Vince

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Kambiz - thanks for the reply, but I already know GSL. As I said in the original post, I'm looking for a simple solution for the generalized eigenvector problem (not regular eigenvector), for the (hopefully relatively simple) 3x3 matrix.

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You need to use the "QZ algorithm"

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the QZ algorithm works in the general case. I thought I had a simpler solution for 3x3 but edited it to remove my comments.

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Thanks yahastu, the QZ algorithm looks interesting.

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If you look more deeply into the QZ algorithm, you will find that in each iteration they use QR iterations on a matrix inverse, which is indirectly computed. You may find that, in the 3x3 case, it is more efficient to just compute the inverse directly using the Laplace Expansion Theorem.

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