# A Problem about Hermitian Form

$$X$$ is a linear space over $$\mathbb C$$,$$q$$ is a nondegenerate $$(X^q=0)$$ Hermitian form on $$X$$. $$V$$ is a subspace of $$X$$,$$V^q= \{x \in X|q(x,y)=0, \forall y \in V \}$$,$$dim X/(V+V^q)$$ is finite, $$(V \cap V^q)^q=V+V^q$$,$$V={v^q}^q$$ ,$$m^-(q)$$ is the dimension of the maximal negative definite subspace of $$q$$.

Please prove :$$m^-(q)=m^-(q|_V)+m^-(q|_{V^q}))+dim (V \cap V^q)$$

I have got no idea about the proof, so I choose to get some help here. Thanks for your instruction.