My question is about ellipsoids.
I have an ellipsoid in 3D centered at zero so it has an equation:
$x^T U \Sigma^2 U^T x = 1$
I know the lengths of it's principal axes (therefore the $\Sigma$ matrix is known). Also I know three points of intersection of ellipsoid with x, y and z axes. How can I find the U matrix?
Thanks in advance!