Triangle Inequality
The triangle inequality states that the length of any side of a
triangle is less than or equal to the sum of the lengths of the other two
sides, with equality occurring only when the triangle degenerates to a
line. In , this becomes
![$\displaystyle \zbox {\Vert\underline{u}+\underline{v}\Vert \leq \Vert\underline{u}\Vert + \Vert\underline{v}\Vert.}
$](http://www.dsprelated.com/josimages_new/mdft/img839.png)
![\begin{eqnarray*}
\Vert\underline{u}+\underline{v}\Vert^2 &=& \left<\underline{u...
...v}\Vert &\leq& \Vert\underline{u}\Vert + \Vert\underline{v}\Vert
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/mdft/img840.png)
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Triangle Difference Inequality
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Cauchy-Schwarz Inequality