Let $I$ be an D1247: Inner product-normed vector space such that

(i)	$\langle \cdot, \cdot \rangle$ is the D34: Inner product in $I$
(ii)	$\Vert \cdot \Vert$ is the D504: Inner product norm in $I$
(iii)	$x_1, \dots, x_N \in I$ is an D9: Orthogonal collection in $I$

Then \begin{equation} \left\Vert \sum_{n = 1}^N x_n \right\Vert^2 = \sum_{n = 1}^N \Vert x_n \Vert^2 \end{equation}