In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance of a vector from the origin is a norm, called the Euclidean norm, or 2-norm, which may also be defined as the square root of the inner product of a vector with itself.
Notation
The p-norm of the \(\vec{v}\) is written as \(\|\vec{v}\|_p\).
L-p norm
\(\|\vec{x}\|_p = (\sum_{i = 1}^n {\lvert \vec{x}_i \rvert}^p)^{\frac{1}{p}}\)
Also see L-one norm, L-two norm.
Bibliography
“Norm (Mathematics).” 2022. Wikipedia, August. https://en.wikipedia.org/w/index.php?title=Norm_(mathematics)&oldid=1103683806.