Suppose we have a 2x3 matrix h, and a 3x4 matrix W such that the product of the two matrices is y.
y=hW
How do we get the Jacobian of y with respect to W? I can get the Jacobian of the individual elements of y i.e. y11, y12 etc with respect to W by taking partial derivatives with respect to each element of W. But each of them is a 3x4 matrix themselves. So, what is the Jacobian of y with respect to W? Is there like a way to combine the 8jacobian matrices of the individual elements of y with respect to W?
Seems like you need to use indicial notation and calculate. Since you are differentiating a matrix wrt another matrix you will end up with a fourth order tensor. You can then list out the matrices, as you say.