Let $V$ be a vector space of dimension $2n$ and $f$ be a non-degenerate skew-symmetric bilinear form on $V$. $V'$ is a subspace of $V$, and the restriction of $f$ on $V'$ is of rank $2k$ for an integer $k$. Then what is the meaning of the integer $n+k-\operatorname{dim}V'$?
This question might not be clear, but in fact, it comes from my considering on the maximal subalgebra of Lie superalgebras.