Undergrad What is the derivative of a matrix transpose?

[dynamicskillingme]

Hi! As the title says, what is the derivative of a matrix transpose?

I am attempting to take the derivative of \dot{q} and \dot{p} with respect to p and q (on each one).

Any advice?

 

[dynamicskillingme]

Also

 

[Mark44]

Hi! As the title says, what is the derivative of a matrix transpose?

I am attempting to take the derivative of \dot{q} and \dot{p} with respect to p and q (on each one).

Any advice?

Your question doesn't make sense to me. You don't take the derivative of a matrix (or a matrix transpose) -- you take the derivative of the functions that make up a vector (or its transpose).

You have $\vec{q} = \begin{bmatrix} q_1 \\ q_2 \\ \vdots\\ q_n \end{bmatrix}$. $\dot{q}$ usually means the derivative with respect to t of $\vec{q}$: $\frac{d\vec{q}}{dt}$.

Without knowing more about this problem, I would guess that $\dot{q}$ is a vector that contains the derivatives (with respect to time) of $q_1, q_2, \dots, q_n$.

In your second post, they are taking partials of H with respect to p and q, not the partials of p or q with respect to each other.