Re: how to find the volume of a quadratic form?

Assuming that A is positive definite (or else you get some kind of 
hyperboloid) it has a cholesky factor L (lower triangular so that
L*L' = A). Then your ellipsoid is the image of { x | x'*x = c} (ie the
sphere of radius sqrt(c)) under inv(L). So its volume is det(inv(L)) times
the volume of the sphere,  Note that det(inv(L)) = 1/det(L) ( =
1/sqrt(det(A))), and L being lower triangular, its determinant is the
product of its diagonal elements. 
Duncan


 
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