A paper has the following equation which I do not understand how to calculate the $\operatorname{diag}$ function:
$$ J = \operatorname{diag}\{ A_1 \otimes A_1, A_2 \otimes A_2, \cdots, A_N \otimes A_1N \} \dot{} \left( Q^T \otimes I_{n^2} \right) $$
The matrices $A_i$ and $Q$ all have the same size $n$. Is the $\operatorname{diag}$ function putting the matrices on the diagonal as blocks just like the Kronecker product does block multiplication?
There's an example on the paper with
$$ A_1 = \begin{pmatrix} 0.5 & 10 \\ 0 & 0.5 \end{pmatrix}\quad A_2 = \begin{pmatrix} 0.5 & 0 \\ 10 & 0.5 \end{pmatrix}\quad Q = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$$
and it then says $J$ has the eigenvalues $$\begin{bmatrix}0.25 & 0.25 & -0.25 & -0.25 & 0.0006 & -0.0006 & 0.4994 & -100.4994\end{bmatrix}$$ Which means it must have the size $n^3$ at the end, if I'm not confusing myself.
$$\text{diag}(A_1,A_2,\dots,A_N)=\begin{pmatrix} A_1 & 0 &\cdots & 0 \\ 0 & A_2 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & A_N \end{pmatrix}$$ is a block matrix where the diagonal terms are given as the arguments of $\text{diag}$.