The signature of a non-degenerate quadratic form Q = y_1^2 + y_2^2 + ... + y_p^2 - y_(p + 1)^2 - y_(p + 2)^2 - ... - y_r^2 of rank r is most often defined to be the ordered pair (p, q) = (p, r - p) of the numbers of positive, respectively negative, squared terms in its reduced form.

p-signature | quadratic | quadratic form rank | Sylvester's inertia law | Sylvester's signature