= Common zero of complex quadratic forms
{title2=$n\ge2^d$}
= Common zeros of complex quadratic forms
{synonym}
Any $d$ <quadratic forms> on $\mathbb C^n$ have a common nonzero zero when $n\ge2^d$. Choose a <totally isotropic subspace> for the first form, of dimension at least $\lfloor n/2\rfloor$. Restrict the remaining forms to it and repeat by induction. After $d$ stages at least one dimension remains. This elementary sufficient bound does not assert that $2^d$ is the best possible threshold.
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