Gram's Inequality

Let $f_1(x)$, ..., $f_n(x)$ be Real Integrable Functions over the Closed Interval $[a, b]$, then the Determinant of their integrals satisfies

$$\left\vert\matrix{ \int_a^b {f_1}^2(x)\,dx & \int_a^bf_1(x)f... ...)f_n(x)\,dx\cr}\right\vert\geq 0.\hrule width 0pt height 9.2pt$$

See also Gram-Schmidt Orthonormalization

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1100, 1979.