In [42]:

    

f = Matrix([cos(th), sin(th), 0])
g = Matrix([0, 0, 1])
xvector = [x,y,th]


    

In [43]:

    

lie_bracket(f,g,xvector)


    

    
Out[43]:





$$\left[\begin{matrix}- \sin{\left (\theta \right )}\\\cos{\left (\theta \right )}\\0\end{matrix}\right]$$

In [44]:

    

span = bracket_span([f,g],xvector)
span


    

    




rank = 3






    
Out[44]:





$$\left [ \left[\begin{matrix}\cos{\left (\theta \right )}\\\sin{\left (\theta \right )}\\0\end{matrix}\right], \quad \left[\begin{matrix}0\\0\\1\end{matrix}\right], \quad \left[\begin{matrix}- \sin{\left (\theta \right )}\\\cos{\left (\theta \right )}\\0\end{matrix}\right]\right ]$$

In [45]:

    

span = list2matrix(span)
span


    

    
Out[45]:





$$\left[\begin{matrix}\cos{\left (\theta \right )} & 0 & - \sin{\left (\theta \right )}\\\sin{\left (\theta \right )} & 0 & \cos{\left (\theta \right )}\\0 & 1 & 0\end{matrix}\right]$$