Here are two n-dimensional vectors: $V_1$ and $V_2$
$V_1 (v_1,v_2, \dots ,v_n)$
$V_2 (v_1,v_2, \dots ,v_n)$
$V_1 \cos(\theta) + V_2 \sin(\theta)$ is an ellipse in the $n$-D space. (Its center is the origin.)
I want to find the directions and magnitudes of the major and minor axes.
I have a $2$-D example here: Ellipse with non-orthogonal minor and major axes?
People used SVD to find the minor and major axes of that $2$-D example, but I'm not familiar with SVD. So I'm having problem extending it to $n$-dimension or arbitrary $V_1$ and $V_2$.
Could anybody give a formula for it? Thank you very much in advance!