3x3 Jacobi Algorithm

Finding eigenvalues and eigenvectors of symmetric matrices is pretty useful. Typically you don't have to implement your own algorithms to do this since there are so many packages around that can do it really well. But there are still times you might want to do it yourself, particularly when dealing with small matrices. For 3x3 matrices there's a simple iterative approach. The technique I use here is called the "Jacobi Algorithm". I used Chapter 3 of Calculus++: The Symmetric Eigenvalue Problem by Eric A Carlen to figure out how to get this working. Check out 2x2 jacobi algorithm for some more information on how this works in the simple 2x2 case.

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