Inverse Vectorization Vec^-1 Hope that you will find this post in good health.
I am Mr. Adnan from Pakistan with research background in Control systems. I am working on one problem in which Hadamard weights are using. 
During solving that problem, i am facing one problem to calculate inverse vectorization/stacking operator i.e $\text{vec}^{-1}$. I would be highly thankful if could you please guide me that how to calculate for example 
$$\text{vec}^{-1}(Wq)$$ 
where $W$ is non singular matrix and $q$ is controller having state space representation 
\begin{align}
X'&=Ax+Bu, \\
Y&=Cx+Du
\end{align}
I just have two queries to calculate above inverse


*

*what should be order of $q$ to calculate inverse vector operator $\text{vec}^{-1}$

*if order of controller $q$ is know then Please tell me how to solve $\text{vec}^{-1}$, any formula,relation or command.
I Knew these two commands $\text{vec}$ and $\text{vec}^{-1}$ but that is not working in my problem.
-Thanks in Advance

I do not really understand what your problem is? 
Let $A$ be defined as:
$$A = \begin{bmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{bmatrix}$$
Then $\operatorname{vec}(A)$ is defined as
$$\operatorname{vec}(A) = \begin{bmatrix} a_{11} \\ a_{21}\\ a_{12} \\ a_{22} \end{bmatrix}$$
As a result the inverse is defined as
$$\operatorname{vec}^{-1}(\operatorname{vec}(A)) = A$$
Now, when I typed this down, I think I understand your problem. You have the matrix $B = Wq$ which is vectorized and want to inverse it. This will only work if you know the size of $W$ and $q$ before they were vectorized. Then you know size which the result should be after the inverse vectorization.
Furthermore, what is $q$ exactly? You say that it is a state space system? What do you imagine the result of $Wq$ to be then?
