Quadratic forms | Field (mathematics)

U-invariant

In mathematics, the universal invariant or u-invariant of a field describes the structure of quadratic forms over the field. The universal invariant u(F) of a field F is the largest dimension of an anisotropic quadratic space over F, or ∞ if this does not exist. Since formally real fields have anisotropic quadratic forms (sums of squares) in every dimension, the invariant is only of interest for other fields. An equivalent formulation is that u is the smallest number such that every form of dimension greater than u is isotropic, or that every form of dimension at least u is universal. (Wikipedia).

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From playlist Classify Polygons

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Isotropic quadratic form | Algebraically closed field | Universal quadratic form | Local field | Linked field | Group (mathematics) | Torsion subgroup | Formally real field | Field extension | Pythagorean field | Mathematics | Field (mathematics) | Global field | Quadratically closed field | Quadratic form | Algebraic curve | Complex number | Parity (mathematics) | Tsen's theorem | Degree of a field extension