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Quadratic Forms
Examples:
-  quadratic curves (circles, ellipses, hyperbolae, parabolae) and surfaces
  (spheres, spheroids, ellipsoids, cones, cylinders, ...);
 -  kinetic energy of solid bodies;
 -  potential energy near equilibria;
 -  ...
 
Matrix form:

An orthonormal transformation leaves the quadratic form unchanged

but can simplify the coefficients.  On principal axes

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 10/09/00 0:40:26
 10/11/00 0:05:25