Computation of the left invariant vector field for SO(3)

[nigelscott]

I am trying to improve my understanding of Lie groups and the operations of left multiplication and pushforward.

I have been looking at these notes:

https://math.stackexchange.com/questions/2527648/left-invariant-vector-fields-example
https://math.stackexchange.com/ques...ate-a-vector-in-a-left-invariant-vector-field
https://math.stackexchange.com/questions/1764479/left-invariant-vector-field-on-so3

I have worked out the following for SO(3).

Is this correct? I am not sure about the appearance of the sin and cos after the matrix multiplication.

 

[fresh_42]

I'm not quite sure what you're going to do. Maybe this here is of interest for you, although the example is $\operatorname{GL}(n,\mathbb{R})$. The code is the comment isn't mine, and SE neither.
https://www.physicsforums.com/insights/pantheon-derivatives-part-iv/