Is there any consensus on what $A_n = O_p(n^{-1})$ means for a sequence of random matrices $\{A_n\}_{n\geq 1} \in \mathbb{R}^{d\times d}$?
Does it mean that the operator (spectral) norm of $A_n$ converges to zero in probability at the rate $n^{-1}$?
Does it mean that the maximum entry of $A_n$ converges to zero in probability at the rate $n^{-1}$?
Is it even correct to write $A_n = O_p(n^{-1})$ when $A_n$ is a random matrix, or is it a sloppy shorthand?