Question 4. Refer the class note on discriminant analysis and definition notations of w, B&S. Show that the w maximizing satisfies wTBw wTSw S1Bw = w (Hence, w is the eigenvector and is eigenvalue of S1B.) Hint: Argue that we can maximize wT Bw subject to wT Sw = a , where a is a constant. Then introduce a Lagrange multiplier for the constraint and differentiate with respect to elements of w.

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