Let $A$ and $B$ be two square matrices of dimension $a$ and $b$. $\text{vec}\left(\cdot\right)$ is the vectorization of a matrix.
Now $v_0=\text{vec}\left(A\otimes B\right)$ is not $v_1=\text{vec}\left(A\right) \otimes \text{vec}\left(B\right)$, but the set of vector elements in both is equal, but $v_0$ and $v_1$ seem to be related by a permutation of elements: $v_0 = P_{a,b} v_1$
Can this permutation matrix $P_{a,b}$ be described in general?