Coordination System Change Matrix

**Tesla2011** · December 17th 2011, 11:26 AM

Let's say we have the default xyz coordination system and want to use the bisectors of the angles of the default coordination system as our new coordination system. What will the transformation Matrix (A) be so that w=A*v, where w,v our old and new systems of coordination respectively

Sorry for syntax errors, but I am not learning math in english, so I am not comfortable with some expressions

**FernandoRevilla** · December 18th 2011, 12:35 AM

Use the following general result: if $B=\{e_1,e_2,e_3\}$ and $B'=\{e'_1,e'_2,e'_3\}$ are basis of $\mathbb{R}^3$ and $e'_i=\sum_{j=1}^3{a_{ij}e_j}$ for $i=1,2,3$ , then $[v]_B=\begin{bmatrix}{a_{11}}&{a_{21}}&{a_{31}}\\{a_{ 12}}&{a_{22}}&{a_{32}}\\{a_{13}}&{a_{23}}&{a_{33}} \end{bmatrix}[v]_{B'}$

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Coordination System Change Matrix

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