Rank (Quadratic Form)

For a Quadratic Form $Q$ in the canonical form

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

the rank is the total number $r$ of square terms (both Positive and Negative).

See also Signature (Quadratic Form)

References

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