= Signature pair of a real symmetric bilinear form
{title2=$(n_+,n_-)$}
= Signature pair
{synonym}
For a real <symmetric bilinear form>, let $n_+$ and $n_-$ be the dimensions of its positive and negative diagonal subspaces. This pair gives the first two components of the <inertia of a bilinear form> and is independent of basis by the <Sylvester's law of inertia>. For a nondegenerate form their sum is the full dimension; otherwise the nullity is an additional invariant. Another convention calls the difference $n_+-n_-$ the <signature of a quadratic form>. The pair convention describes the positive and negative harmonic spaces of the <real de Rham intersection form in dimension four>.
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