I have a matrix (in this case it's a vector but it could be a matrix) $\alpha$.
$$\alpha'=(-0.086877710\quad03767617)$$
In the paper describing the methodology I try to implement, this definition is given.
$$\alpha'\alpha^\bot=0$$
where $\alpha^\bot$ is the orthogonal complement of $\alpha'$ but I have no idea how to solve for $\alpha^\bot$
I am a programmer and not a mathematician so this is not really my terrain. I am working in Python by the way.