I am dealing with $\ell_\infty$ norms, and I need a "mathematical" way to take a vector of $p$ length (We'll call it $x$), and construct a vector pointing in the direction of $\|x\|_\infty$.
I know in English, I can say "And I then construct $\hat x$ such that $\hat x$ is pointing in the direction of the the maximum component of $x$"...... but I'd like a mathematical way to present that.
Thank you all!
EDIT: To be more clear, what I want to happen is all elements of the vector that are NOT equal to the $\ell_\infty$ norm be set to zero.