Is there a characterization of linear isomorphisms of the space of skew symmetric matrices?

Question

Let $M_n^s$ denote the $\scriptstyle\binom{n}{2}$ dimensional space of $n \times n$ skew-symmetric matrices. Is there a characterization of linear isomorphisms that take $M_n^s$ into itself. If $n=2$ then any isomorphism $$Q:M_n^s\rightarrow M_n^s$$ is of the format $$Q(X)=k X.$$