recently I stumbled upon the problem of defining a diagonal matrix whose elements are identity matrices of $dim = n$, where $n$ is the column/row index. For example, for $n=3$:
$\mathbb{I}_3 = \left[{\begin{array}{ccc} I_1 & 0 & 0 \\ 0 & I_2 & 0 \\ 0 & 0 & I_3 \end{array} }\right]$,
and the subscript indicates the size of the matrix, i.e., $I_2$ is a $2\times 2$ identity matrix and so on.
This definition may look silly, but I need a matrix with this property to explicitly define the direct sum of matrices with a notation that's more usual than $\bigoplus_i^n$.
So, $\mathbb{I}_n$ does have a special name?