What is the derivative of a matrix transpose?

In summary, the conversation discusses taking the derivative of a matrix transpose and taking partial derivatives of functions with respect to certain variables. The speaker also clarifies the concept of taking the derivative of a matrix and provides advice on how to approach the problem.
  • #1
dynamicskillingme
27
0
Hi! As the title says, what is the derivative of a matrix transpose?

e0105b10b69da68fd563eb3008f2319c.png

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

Any advice?
 
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  • #2
Also
1c3f5e999304f25920fca3a3694e2ea0.png
 
  • #3
dynamicskillingme said:
Hi! As the title says, what is the derivative of a matrix transpose?

e0105b10b69da68fd563eb3008f2319c.png

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.
 

What is the derivative of a matrix transpose?

The derivative of a matrix transpose is the transpose of the derivative of the original matrix.

What is the purpose of taking the derivative of a matrix transpose?

The derivative of a matrix transpose is useful in calculating the gradient of a function that involves a matrix transpose. It is also used in optimization and linear algebra.

Is the derivative of a matrix transpose always defined?

No, the derivative of a matrix transpose is only defined when the original matrix is differentiable.

How is the derivative of a matrix transpose calculated?

The derivative of a matrix transpose is calculated by taking the derivative of each element in the matrix and then transposing the resulting matrix.

Does the chain rule apply to the derivative of a matrix transpose?

Yes, the chain rule can be applied to the derivative of a matrix transpose when it is part of a larger function that involves other matrices or functions.

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