I have a linear operator with its matrix in certain coordinates to be
$ \begin{pmatrix} 1 & 0 & 0 & \cdots & 0 \\ 0 & \frac{1}{2} & 0 & \cdots & 0 \\ 0 & 0 & \frac{1}{3} & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \\ 0 & 0 & 0 & \cdots & \frac{1}{n} \end{pmatrix} $
What is this linear operator? How could I construct it without referring to coordinates?