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Thread: Coordination System Change Matrix

  1. #1
    Dec 2011

    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
    Nov 2010
    Madrid, Spain

    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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