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  "body": "\n## Summary\n\nA quadratic form on a vector space is a map $Q$ to the scalars with $Q(av) = a^2 Q(v)$.\nAlso, $Q(u + v) - Q(u) - Q(v)$ must be bilinear in $u$ and $v$.\nIn coordinates, it is a homogeneous polynomial of degree two.\n",
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