normierter

Normierter is a German adjective derived from normieren (to normalize, standardize). It denotes that something has been brought into a normalized form or conforming to a norm. The term is common in technical and scientific writing and can function both attributively and predicatively.

In mathematics and physics, normierter Vektor refers to a vector with unit length, i.e., a vector v with ||v|| = 1. The normalized vector is obtained by dividing the vector by its norm: v_hat = v / ||v|| for v ≠ 0. In this context, normalization often aims to focus on direction rather than magnitude. In statistics and data processing, normierte Daten or normierte Werte describe data that have been rescaled to a common range or standard form, such as min–max normalization to [0,1] or z-score normalization to zero mean and unit variance.

In computing and numerical analysis, normierte numbers describe floating-point values stored in normalized form, typically with the leading digit of the significand nonzero, which supports a unique representation. The term declines according to German grammar: normierter, normierte, normiertes. Outside specialized contexts, synonyms like normalisiert or standardisiert are sometimes preferred, depending on the exact meaning. Related concepts include Normalisierung (normalization) and Normierung (standardization).