I am currently reading a section in a book in which a certain proof connects two multivariate random distributions. While the mean makes sense to me, I don't quite understand how the author arrives at the reported covariance matrix. The equation in question is the following:
$$\mathcal{N}_{conc.}\left(\left(\matrix{\mathbf{x_{t}} \\ \mathbf{x}_{t+1}}\right)|\mathbf{\mu}_{conc.},\mathbf{P}_{conc.}\right)=\mathcal{N}_{\mathbf{x}_{t+1}}\left(\mathbf{x}_{t+1}|\mathbf{A}\mathbf{x}_{t},\mathbf{Q}\right)\mathcal{N}_{\mathbf{x}_{t}}\left(\mathbf{x}_{t}|\mathbf{m}_{t},\mathbf{P}_t\right)$$
where we have:
$$\mathbf{\mu}_{conc.}=\left(\matrix{\mathbf{m}_{t} \\ \mathbf{A}\mathbf{m}_{t}}\right)$$
$$\mathbf{P}_{conc.}=\left(\matrix{\mathbf{P}_{t} & \mathbf{P}_{t}\mathbf{A}^T \\ \mathbf{A}\mathbf{P}_{t} & \mathbf{A}\mathbf{P}_{t}\mathbf{A}^T+\mathbf{Q}}\right)$$
What is the rule for obtaining this concatenated covariance matrix?