I need to minimize
,
where x, a and are vectors in .
My Idea was to take the derivative, set it to zero and solve for x, but I'm not good in matrix calculus. I would be extremely thankful if somebody could help me here!
you can just combine a and $\mu$ into
$c=a-\mu$ and then find $x$ to minimize
$\dfrac {\|c\cdot x\|^2}{\|x\|^2}$
This is clearly minimized if $x$ is orthogonal to $c$
As $c\in \mathbb{R}^n$ there is an (n-1) dimensional subspace containing all these vectors orthogonal to $c$