It depends upon the n eigenvectors which you are taking corresponding to top n eigenvalues. If you take n more than 1 (say 2) then you will reduce data set to 2 dimensions. Normally when classes are more than 2 then n is taken more than 1 and its called Multiple Discriminate Analysis. I think you know from where to take the eigenvectors, if not then you can ask that too. Once you have the reduced data, apply any classification technique to build the model and test it.