What is 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 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 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.