# Coordination System Change Matrix

Printable View

• Dec 17th 2011, 11:26 AM
Tesla2011
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
• Dec 18th 2011, 12:35 AM
FernandoRevilla
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 $[v]_B=\begin{bmatrix}{a_{11}}&{a_{21}}&{a_{31}}\\{a_{ 12}}&{a_{22}}&{a_{32}}\\{a_{13}}&{a_{23}}&{a_{33}} \end{bmatrix}[v]_{B'}$