ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Function
Unsigned function
Unsigned Realll func function
Definition D5950
Complex euclidean P-length function
Formulation 0
Let $\mathbb{C}^N$ be a D5640: Set of euclidean complex numbers.
Let $|\cdot| : \mathbb{C} \to [0, \infty)$ be the D1210: Complex modulus function.
The complex euclidean P-length function on $\mathbb{C}^N$ with respect to $p \in (0, \infty)$ is the D4365: Unsigned Realll func function \begin{equation} \Vert \cdot \Vert_p : \mathbb{C}^N \to [0, \infty), \quad \Vert z \Vert_p = \left( \sum_{n = 1}^N |z_n|^p \right)^{1 / p} \end{equation}
Children
Complex euclidean length function
Euclidean P-length function