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Example:
Consider the vector-difference example shown in Fig.5.7. The norm of the difference vector $ w=x-y$ is

$\displaystyle \Vert w\Vert \isdef \Vert x-y\Vert \isdef \Vert(2, 3) - (4, 1)\Vert
= \Vert(-2, 2)\Vert = \sqrt{(-2)^2 + (2)^2} = 2\sqrt{2}.
$

Figure 5.7: Length of a difference vector.
\includegraphics[scale=0.7]{eps/vecdist}


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-21 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA