Following Given 3 orthogonal vectors how to calculate the ellipsoid induced by them?
Assume an arbitrary point $x_0$ and an ellipsoid defined as $(x-v)^t A (x-v) = 1$
Where the ellipsoid's principal axis matrix is given by: $W = [w_1 | w_2 | w_3]$ s.t. $W^t W = I$.
- How to project $x_0$ on the ellipsoid surface?
- How to project $x_0$ on the ellipsoid's principal axes?