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I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$$R_A^C=R_A^BR_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

$R_A^C$ must for a 2x2 matrix be defined as $$ R_A^C= \left( \begin{matrix} xa⋅xb & xa⋅xb \\ ya⋅yb & ya⋅yb \end{matrix} \right) $$

$x_a, y_a and x_b,y_b$ are coordinates for points given in different coordinate frame. I don't see how, using this standard, the multiplication stated above will give the same matrix as for $R_A^C$. Some form for clarification would be helpful here.

I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

$R_A^C$ must for a 2x2 matrix be defined as $$ R_A^C= \left( \begin{matrix} xa⋅xb & xa⋅xb \\ ya⋅yb & ya⋅yb \end{matrix} \right) $$ I don't see how, using this standard, the multiplication stated above will give the same matrix as for $R_A^C$. Some form for clarification would be helpful here.

I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^BR_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

$R_A^C$ must for a 2x2 matrix be defined as $$ R_A^C= \left( \begin{matrix} xa⋅xb & xa⋅xb \\ ya⋅yb & ya⋅yb \end{matrix} \right) $$

$x_a, y_a and x_b,y_b$ are coordinates for points given in different coordinate frame. I don't see how, using this standard, the multiplication stated above will give the same matrix as for $R_A^C$. Some form for clarification would be helpful here.

I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

So.. $R_A^C$ must for a 2x2 matrix be defined as $[xa⋅xb ~~~ xa⋅xb ~~~~ ; ~~~~ ya⋅yb ~~~ ya⋅yb]$ $$ R_A^C= \left( \begin{matrix} xa⋅xb & xa⋅xb \\ ya⋅yb & ya⋅yb \end{matrix} \right) $$ I don't see how, using this standard, the multiplication stated above will give the same matrix as for $R_A^C$. Some form for clarification would be helpful here.

I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

So.. $R_A^C$ must for a 2x2 matrix be defined as $[xa⋅xb ~~~ xa⋅xb ~~~~ ; ~~~~ ya⋅yb ~~~ ya⋅yb]$ I don't see how, using this standard, the multiplication stated above will give the same matrix as for $R_A^C$. Some form for clarification would be helpful here.

I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

$R_A^C$ must for a 2x2 matrix be defined as $$ R_A^C= \left( \begin{matrix} xa⋅xb & xa⋅xb \\ ya⋅yb & ya⋅yb \end{matrix} \right) $$ I don't see how, using this standard, the multiplication stated above will give the same matrix as for $R_A^C$. Some form for clarification would be helpful here.

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I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

So.. $R_A^C$ must for a 2x2 matrix be defined as $[xa⋅xb ~~~ xa⋅xb ~~~~ ; ~~~~ ya⋅yb ~~~ ya⋅yb]$ I don't see how, using this standard, the multiplication stated above will give the same matrix as for RCA$R_A^C$. Some form for clarification would be helpful here.

I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

So.. $R_A^C$ must for a 2x2 matrix be defined as $[xa⋅xb ~~~ xa⋅xb ~~~~ ; ~~~~ ya⋅yb ~~~ ya⋅yb]$ I don't see how using this standard the multiplication stated above will give the same matrix as for RCA. Some form for clarification would be helpful here.

I am the moment learning about rotation matrices. It seems confusing how it could be that $R_A^C=R_A^B⋅R_B^C$ is the rotation from coordinate frame A to C C to A, and A,B,C are different coordinate frames.

So.. $R_A^C$ must for a 2x2 matrix be defined as $[xa⋅xb ~~~ xa⋅xb ~~~~ ; ~~~~ ya⋅yb ~~~ ya⋅yb]$ I don't see how, using this standard, the multiplication stated above will give the same matrix as for $R_A^C$. Some form for clarification would be helpful here.

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