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In this part of the lecture FDA for 2 classes is described, however you can find the discribtion for k classes in the next pages which is referred to as FDA for multi class problems. The equations here are correct for two class case and you can find for multi class in the following pages, in multiclass case since W is not a vector anymore (it is a matrix) therefore instead of max (WT SB W / WT SW W) , it should be written as max (Tr (WT SB W) / Tr (WT SW W)).