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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


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

© 1996-9 Eric W. Weisstein