Alternative notation for maximum of a vector.

Question

Do you know of a one symbol notation for $\max(\mathbf{x}), \mathbf{x}\in\mathbb{R}^n$ ?

For instance the mean is often denoted with an overline: $\overline{\mathbf{x}}$.

Alternatively, is the maximum associated to a letter or symbol, like the letter $\mu$ that often denotes the mean ?

Answer 1

There is the $\ell_\infty$ norm, which coincides with the maximum if the vector has nonnegative entries: $$ \| x\|_\infty = \max_{1\leq k\leq n} |x_k| $$

For the maximum of a statistical sample (of size $n$) specifically, you are looking for the $n$-th order statistic: $$ X_{(n)} = \max\{X_1,\dots,X_n\} $$