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A common way is to make use of the Schwarz inequality. First note that: $$\frac{|w^Hd|^2}{w^HQw} = \frac{|w^HQ^{1/2}Q^{-1/2}d|^2}{w^HQw}$$ Using the Schwarz inequality on the numerator: $$\frac{|w^HQ^{1/2}Q^{-1/2}d|^2}{w^HQw} \leq \frac{(w^HQw)(d^HQ^{-1}d)}{w^HQw} = d^HQ^{-1}d$$ Thus, $$\frac{|w^HQ^{1/2}Q^{-1/2}d|^2}{w^HQw} \leq d^HQ^{-1}d$$ From this, it ...