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The tensor product of maps named for this adjective is used to give a ring structure to the Witt group of a field. The Hasse–Minkowski theorem concerns the equivalence of maps named for this adjective. The number of positive and negative entries in matrices that represent maps named for this adjective is the signature, which is invariant by Sylvester’s law of inertia. Given a matrix B, a scalar-valued form named for this adjective is defined by mapping x to [read slowly] “x-transpose times B times x.” A theorem named for this adjective gives the product of the Legendre symbols of “p over q” times “q over p” as negative one to an appropriate power. That law was proved by Gauss and is named for this adjective and reciprocity. For 10 points, name this adjective that describes polynomials of degree two. ■END■
ANSWER: quadratic [accept quadratic forms or quadratic reciprocity or quadratics; prompt on bilinear forms by asking “what kind of forms are bilinear forms used to define”; reject “linear”]
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