I have a question about the process for finding the optimal subspaces for LDA.
A detailed process can be found in 114p. of 'The Elements of Statistical Learning'
I want to know what the role of 'Whitening Transformation' in this process is.
I think that we can just use the original class centroids matrix $M$ instead of $M^*=MW^{-1/2}$, because the goal is to get principal components for the matrix $M$. Why do we have to take this kind of transformation?