# Non-symmetric matrix projection

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• Jul 16th 2009, 05:24 AM
lep11
Non-symmetric matrix projection
I am performing minimization for a N=10 parameter function. If I have, say, 100 trial solution vectors, where each solution vector is a row in $\mathbf{A}$, my goal is to use the top 10 solutions to form a 10 x 10 matrix $\mathbf{S}$, perform eigenanalysis on it, and then get the eigenvectors to reflect which step direction the group of solutions is heading. Certainly, $\mathbf{S}$ is not symmetric, so I would need to solve the general eigenvalue problem for a real non-symmetric matrix.

In order to find the single direction of the solutions, wouldn't I need to add together the eigenvectors for the 2 greatest eigenvalues? Basically, how can I obtain the single vector reflecting the single direction in which the top 10 solutions are heading?