L-infinity norm

Maximum/Supremum/Chebyshev/ $L_{\infty }$ norm

The supremum norm of a bounded function $f$ defined on a domain $D$ is given by:

$$||f|{|}_{\infty }=\underset{x\in D}{\sup }|f(x)|$$

For a finite-dimensional vector space, the maximum norm of a vector $x\in {\mathbb{R}}^n$ is defined as:

$$||x|{|}_{\infty }=\underset{1\le i\le n}{\max }|x_i|$$

The norm measures the largest absolute value among the components of the vector.