Suppose we have the following function for the positive part of a real number, which we define as:
$ f : \mathbb{R} \to \mathbb{R} $
$f(x)=\max(x,0)$
And we generalize this function to matrices trivially by applying it elementwise
$ f : \mathbb{R}^{m \times n} \to \mathbb{R}^{m \times n} $
$ (f(A))_{i,j}=\max((A)_{i,j},0) $
The function $ f $ is obviously nonlinear on the space of $ m \times n $ matrices but as sometimes done with nonlinear operators I was hoping that perhaps I can embed the space into higher dimensions where I can represent $ f $ as a linear operator and then go back to the original space in a nonlinear fashion by clipping the unneeded terms. I would certainly appreciate all help on this and I kindly appreciate all efforts to of helpers.