Let $A \in \mathbb{C}^{N \times M}$ and $D \in \mathbb{C}^{M \times M}$ each be a D999: Complex matrix such that

(i)	$A_1, A_2, \ldots A_N \in \mathbb{C}^{1 \times M}$ are each a D5688: Complex row matrix
(ii)	\begin{equation} A = \begin{bmatrix} A_1 \\ A_2 \\ \vdots \\ A_N \end{bmatrix} \end{equation}
(iii)	\begin{equation} D = \begin{bmatrix} D_1 & 0 & \cdots & 0 \\ 0 & D_2 & \vdots & 0 \\ \vdots & \cdots & \ddots & \vdots \\ 0 & 0 & \cdots & D_M \end{bmatrix} \end{equation}

Then \begin{equation} D A = \begin{bmatrix} A_1 D_1 \\ A_2 D_2 \\ \vdots \\ A_N D_N \end{bmatrix} \end{equation}