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Math Help - Coordination System Change Matrix

  1. #1
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    Coordination System Change Matrix

    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
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Coordination System Change Matrix

    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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