= Isotropic dimension bound from real inertia
{title2=$\dim U\leq\min(p,q)$}
For a nondegenerate real <quadratic form> of inertia $(p,q)$, projection of a totally isotropic subspace onto either its positive or negative coordinate subspace is injective: a vector with one projection zero would have strictly one-signed quadratic value unless it vanished. Thus its dimension is at most both $p$ and $q$. This bound is attained by pairing one positive and one negative coordinate for each of $\min(p,q)$ independent null vectors.
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