(Terminology) Operation taking matrices to a block matrix

Question

What is the name of the map defined by $$ \begin{aligned} \operatorname{Mat}_{n\times m} & \rightarrow \operatorname{Mat}_{kn\times km}\\ (A_1,\dots,A_k) & \mapsto \begin{bmatrix} A_{1} & 0 & 0 \\ 0 & A_2 & 0 \\ \dots \\ 0 & \dots & A_{k} \end{bmatrix} \end{aligned} $$

Answer 1

It is called a direct sum. The direct sum of $A_1,A_2,\ldots,A_k$ is usually denoted by $A_1\oplus A_2\oplus\cdots\oplus A_k$ or $\bigoplus_{i=1}^kA_i$.