# $\infty$-norm Motivation: An interesting [[Vector Norms|vector norm]] case. The infinity-norm of a vector $\vec{x}$ is denoted $||\vec{x}||_\infty$, and is defined as the maximum of the absolute values of its components. For a vector $\vec{v} = (1, 3, -6)$, $||\vec{v}||_\infty = \{max:|1|, |3|, |-6|\} = 6$ This is more of colloquial norm compared to other common forms of norms, like the [[2-norm]], since it's hard to mathematically visualize $||\vec{x}||_\infty \left[\sum_{n} |\vec{x}|^\infty \right]^{1/\infty} $ so just consider it to be a measure of the maximum absolute value of a vector :] .