note
randyk
I was thinking of the problem differently -
find the extremal points of
<tt>x<sup>†</sup>Dx</tt>, which leads to the eigenvalue
equation <tt>Dx = 0</tt>. This equation doesn't determine
<tt>x<sup>†</sup>x</tt> completely, so one is free to impose, for example, <tt>x<sup>†</sup>x = 1</tt> as a
normalization condition. But you're right that if
<tt>x<sup>†</sup>x = 1</tt> is intended as a true constraint, then a method like Lagrange multipliers should be used.
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