Quadratic Forms




     The sums of squares when computing <x,x>.  


     The minimization of quadratic forms with linear terms can be
done  in  closed  form with the minimizer obtained by zeroing the
gradient.


     Quadratic forms occur frequently in applications  of  linear
algebra  to  engineering (optimization) and signal processing (as
output noise power). They also arise in physics (as potential and
kinetic energy), differential geometry (as  normal  curvature  of
surfaces),  economics  (as utility functions), and statistics (in
confidence ellipsoids)


     A quadratic form is a function Q whose value at a  vector  x
can be computed by an expression of the form Q(x) = xAx.