Sorry for boring you my friends during spring holiday. I am haunted by a question of matrix differentiation.
$\textbf{R}$ is a matrix of dimension $3\times3$. It is parametrized by three variables $a$, $b$ and $c$. I would like to form the variational form of this matrix. My trial is given by
$$\delta \textbf{R} = \frac{\partial \textbf{R}}{\partial a} \delta a + \frac{\partial \textbf{R}}{\partial b} \delta b + \frac{\partial \textbf{R}}{\partial c} \delta c$$
I have serious doubt about this expression. Thank you for taking a look.