Given that we would like the classes (or 𝒚 ! and 𝒚 " ) to be as far apart as possible (or the difference between the classes should to be maximized), we want to maximize the quantity (𝝁 1 ! -𝝁 1 " ) " , where 𝝁 1 % (i = 1,2) denotes the matrix that represent the projected mean of class 𝒚 % (i = 1,2). ) " as: