Thread Subject: Fisher Linear Discriminant Analysis eigen vector

Hi,

I need to do FLD on a dataset with 5000 samples and 500 features belonging to two classes.
I implemented the FLD with the standard formulas computing the within class and between class scatter matrix and eigenvalues.

I end up with something like [eigen,lambda] = eig(pinv(SW)*SB);
eigen has 500x500 dimension, and eigen(1,:)
should be the first component of FLD, am I right?

As far as I understand it should contain my data reduced to the one-dimensional space.
On this data I then have to train a classifier and see how it performs.

But I don't understand what I have to do to on the 5000 samples with this eigen matrix.

Because if I do PCA with processpca I get as result a 500x5000 matrix where
(1,:) is my first principal component of my data.

How do I acheive this with the eigenvector I have (get the 5000 points reduced to the first dimension).

Thanks for any hint