Indefinite Quadratic Form

A Quadratic Form $Q({\bf x})$ is indefinite if it is less than $0$ for some values and greater than $0$ for others. The Quadratic Form, written in the form $({\bf x}, {\hbox{\sf A}}{\bf x})$, is indefinite if Eigenvalues of the Matrix ${\hbox{\sf A}}$ are of both signs.

See also Positive Definite Quadratic Form, Positive Semidefinite Quadratic Form

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1106, 1979.