How to represent a given equation more clear, profressional and short form?
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.