I am fairly new to matrix algebra and I do not know how to derive this step. I am reading this report of Quaternion Kinematics: http://www.iri.upc.edu/people/jsola/JoanSola/objectes/notes/kinematics.pdf
In the page 16, it takes the expression:
$\dot{\mathbf{R}^\intercal}\mathbf{R}+\mathbf{R}^\intercal \dot{\mathbf{R}}=0$,
and reduces it to:
$\mathbf{R}^\intercal\dot{\mathbf{R}}=-(\mathbf{R}^\intercal\dot{\mathbf{R}})^\intercal$,
These are rotation matrices. What steps are in between?
Thanks in advance
Observe $$\dot{R}^TR+R^T\dot{R}=0\Rightarrow R^T\dot{R}=-\dot{R}^TR$$ and use $A=(A^T)^T$ and then $(AB)^T=B^TA^T$ to obtain $$\dot{R}^TR=\left(\left(\dot{R}^TR\right)^T\right)^T=\left(R^T\left(\dot{R}^T\right)^T\right)^T=\left(R^T\dot{R}\right)^T.$$