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An eigenvector of an operator is a vector such that the action of the operator is the same as multiplication by a constant, called the eigenvalue. The eigensystem of an operator is the set of all such eigenvectors and their associated eigenvalues.

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From geometrical tools (www.geometrictools.com) http://www.geometrictools.com/Documentation/EigenSymmetric3x3.pdf I hope this helps
answered Jun 6 '13 by Tom