Signature (Quadratic Form)

The signature of the Quadratic Form

$$Q={y_1}^2+{y_2}^2+\ldots+{y_p}^2-{y_{p+1}}^2-{y_{p+2}}^2-\ldots-{y_r}^2$$

is the number $p$ of Positive squared terms in the reduced form. (The signature is sometimes defined as $2p-r$.)

See also p-Signature, Rank (Quadratic Form), Sylvester's Inertia Law, Sylvester's Signature

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1105, 1979.