I have a given $A_{m \times n}$ matrix whose $i, j$th component is $a_{ij}$, let $$\mu = \max \{ a_{ij} : 1 \leq i \leq m, 1 \leq j \leq n\}$$
Let $J_{m \times n}$ be the $m \times n$ matrix whose $i, j$th component is $1$: that is, the all-ones matrix. (This notation isn't quite standard, but it's as close to standard as I know. $J$ is often the all-ones matrix)
Thus, I have an expression such as (With helping from Patrick Stevens)
$$\mu J_{m \times n} - A$$
However, it is so many sentences for expression the above equation. Do we have more short and standard way to represent it? As my found, the $J_{m \times n}$ can be
$$\max (A_{m\times n})\times 1_A-A$$
where $1_A$ is Indicator function
Does it equivalent with original meaning?