How to represent a given equation more clear, profressional and short form? I have a image $U_{m \times n}:\Omega \to \mathbb R^2$, the output $P$ can be define as
 $$P=\mu J_{m \times n} - U$$
where $\mu = \max \{ u_{ij} : 1 \leq i \leq m, 1 \leq j \leq n\}$, $J_{m \times n}$ 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)

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 expressed by indicator function such as

$$P=\max (U)\times 1_{\Omega}-U$$

where $1_{\Omega}$ is Indicator function

Does it equivalent with original meaning? If not, please give me a standard and common expression in image processing. Thanks
I think the notation $J_{m,n}$ is pretty standard for an all-ones matrix. So the only possible clarification would be to dispense with $\mu$ and directly specify what it actually is:

$$P=||U||_{\max}J_{m,n}-U$$

where $||.||_{\max}$ denotes the max norm of a matrix.