I have a several 3D vectors $X_{i}$ which lay approximately in a plane. Now I need to find a single vector, which is normal (as much as possible) to all of them.
For two vectors, I can use a cross product to obtain such vector.
For multiple vectors, I found this formula:
$\left( \sum_{i=1}^{n} X_{i}X_{i}^{\textbf{T}} \right)u=0$
Here $u$ is the desired vector (null vector of a covariance matrix).
Question: What is the reason behind this formula?