just a quick question that is very simple but somewhat hard to explain. I am using 4 specific eigenvalues of a large 80x80 k-dependant matrix. I found the 4 eigenvalues of interest for various k and sorted them in 4 distinct lists as need them. Now I am interested in their eigenvectors.
My question is, is there a way, other than Solve, to get the eigenvector to ONE specific eigenvalue. I guess I could use Eigensystem, let Mathematica find all 80 again and the pick the EVec corresponding to the Eval already found. This seems somewhat stupid though, because I don't need the 79 others.
On the other hand Solve looks also like overcomplicating the problem as well, as I am not using an inbuilt Algorithm to find Eigenvectors anymore. Besides my first tries here weren't successful at all, giving me error messages saying something about badly conditioned matrices giving large numerical error.
Help would be much appreciated! Thanks
EDIT1: Using Eigensystem showed me that the results for eigenvalues by Eigenvalue are different in the 16th digit than the results for Eigensystem!! Why is that! And how to get around that?