Is there a notation for multiplying block matrix by "scalar" matrix (ie multiply each block individually)?

Question

Is there a notation for the question mark place? A and B are standard real general matrices. AB means standard matrix multiplication of A and B.

$$ \begin{pmatrix} AB & AB \\ AB & AB \end{pmatrix} = A \, ? \, \begin{pmatrix} B & B \\ B & B \end{pmatrix} $$

Answer 1

Note that blockwise multiplication by $A$ is the same as multiplying by the block-diagonal matrix $$\begin{bmatrix} A & 0 \\ 0 & A \end{bmatrix}.$$ In the past, I've used various notations to refer to the above, such as $[[A]]$ and Diag($A$), and just made sure to define my notation before using it.

That said, I'm also curious whether a standard notation exists.