Does this row permutation of stacked identity matrices have a name?

Question

Does this matrix have a specific name: $$\begin{pmatrix} 1 & 0 & \cdots & 0 \\ \vdots & 0 & & 0 \\ 1 & 0 & & 0 \\ 0 & 1 & & 0 \\ 0 & \vdots & & 0 \\ 0 & 1 & & 0 \\ 0 & 0 & \ddots \\ 0 & 0 & & 1 \\ 0 & 0 & & \vdots \\ 0 & 0 & & 1 \end{pmatrix}?$$

Answer 1

This matrix does not have a name that I know of. However, it can be nicely written as the Kronecker product $M = I \otimes x$ where $I$ is an identity matrix and $x$ is the column-vector $x = (1,\dots,1)^T$.

If you simply wanted to stack identity matrices, that would instead be the product $x \otimes I$.