I have the following question:
Let $V$ be a finite dimensional complex vector space. For a given bilinear form $(,): V \times V \rightarrow \mathbb{C}$, a subspace $W$ of $V$ is called isotropic with respect to $(,)$ if $(w,w) =0$ for all $w\in W$.
My questions are that：
(1). Is it true that the dimension is invariant? (I mean, it is a constant for all isotropic subspaces).
(2). How can we describe this dimension in terms of any information of $(,)$?
(3). How can we find a maximal isotropic subspace? Thanks very much!