Trait maths_traits::analysis::metric::Norm

pub trait Norm<K: UnitalRing, X: RingModule<K>, R: Real>: Seminorm<K, X, R> { }

A real-valued on a ring-module that quantifies it's length, disallowing null-vectors

Specifically, a norm ‖x‖ is a function from a ring module X over K to the reals such that:

• K has a norm |•|
• ‖x‖ > 0 for all x != 0
• ‖cx‖ = |c|‖x‖
• ‖x+y‖ <= ‖x‖ + ‖y‖

This is distinct from a Seminorm in that it is not allowed to be 0 for non-zero vectors

Implementors

impl<K: ComplexRing, V: InnerProductSpace<K>> Norm<K, V, <K as ComplexSubset>::Real> for InnerProductMetric

Loading content...