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)	$A_1, A_2, \, \ldots, \, A_M \in \mathbb{C}^{N \times 1}$ are each a D5689: Complex column matrix
(ii)	\begin{equation} A = \begin{bmatrix} A_1 & A_2 & \cdots & A_M \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} A D = \begin{bmatrix} A_1 D_1 & A_2 D_2 & \cdots & A_M D_M \end{bmatrix} \end{equation}