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how to transform a cylinder from a coordinate system having orthogonal basis vectors $v_1$, $v_2$ and $v_3$ into another a coordinate system having orthogonal basis vectors $\begin{pmatrix}1\\0\\0\end{pmatrix}$, $\begin{pmatrix}0\\1\\0\end{pmatrix}$ and $\begin{pmatrix}0\\0\\1\end{pmatrix}$.

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    An example would help.2012-02-09
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    So would a better formed question. Are you asking about a rotation of a coordinate system?2012-02-09
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    Your question literally asks how to transform a cylinder into a coordinate system. :-\.2012-02-09

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