$$\dot \xi = - (L_{n} \otimes I_{m}) \xi$$
This equation is commonly cited in works about the distributed consensus of cooperative control, in fact, it's the matrix form of the basic consensus algorithm
I just got confused with dimensions of matrices, It's already given that $\epsilon$ is $n \times m$, so is $\dot \epsilon $, but what is confusing is that the Kronecker product gives an $n m \times n m$, so normally we can't have a matrix product between $n m \times n m$ matrix and an $n \times m$ one, dimensions don't match! Can one clarify this for me, please