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Scalar multiplication

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The vector $ s\vec{a}$ corresponds to an '$ s$ -fold' translation, that is

$\displaystyle s\left(\begin{array}{c}a_1\\ a_2\\ a_3\end{array}\right) = \left(\begin{array}{c}sa_1\\ sa_2\\ sa_3\end{array}\right)\, . $

Particularly, we have $ 0\vec{a}=\vec{0}$ .
\includegraphics[width=7.4cm]{a_smult.eps}
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  automatically generated 3/28/2008