L2-Norm

A Vector Norm defined for a Vector

$${\bf x} = \left[{\matrix{x_1\cr x_2\cr \vdots\cr x_n\cr}}\right],$$

with Complex entries by

$$\vert\vert{\bf x}\vert\vert _2=\sqrt{\sum_{r=1}^n \vert x_r\vert^2}\,.$$

The $L_2$-norm is also called the Euclidean Norm. The $L_2$-norm is defined for a function $\phi(x)$ by

$$\vert\vert\phi\vert\vert^2 \equiv \phi\cdot\phi \equiv \left... ...{\phi\vert\phi}\right\rangle{}\equiv \int^b_a [\phi(x)]^2\,dx,$$

See also L1-Norm, L2-Space, L(infinity)-Norm, Parallelogram Law, Vector Norm

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, pp. 1114-1125, 1979.