i thought to myself, is it worth the time to try and find an eigenvalue of a matrix, that the app multiply in vectors a lot, so that the multiplication will be faster, has anybody thought about that?

Hmm, I can''t really answer that offhand because you didn''t provide much information on how and why you''d be using the eigenvalues and where you''d be getting them from.
In general, it''s always best to simplify frequently used calculations. But usually, matrices used in transformations are already simplified (assuming they''re designed well) and finding the eigenvalues won''t give you anything better than you already have. It seems to me that if you think calculating eigenvalues would be a speed gain, you need to examine your storage of matrices and why the representation is complex.