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. In the event that the quadratic form Q is allowed to be degenerate, one may write Q = y_1^2 + ... + y_p^2 - y_(p + 1)^2 - ... - y_(p + q)^2 + y_(p + q + 1)^2 + ... + y_(p + q + z)^2 where the nonzero components y_(p + q + 1), ..., y_(p + q + z) square to zero. In this case, the signature of Q is most often denoted by one of the triples (p, q, z) or (z, p, q).

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