Is there any name for a square, symmetric matrix, created in the following format:
$$M_{i,j} = \left\{\begin{matrix} i + j & i \neq j\\ 0 & i = j \end{matrix}\right.$$
where $i, j$ start with 1. In particular I am looking whether there are any interesting properties and applications this matrix. I tried to search through this list of matrices, but nothing looks like mine.