HilbertSpace concept

Description

A Hilbert space is a BanachSpace, equipped with an inner product, denoted by <y,x> where the norm is induced from the inner product as ||x|| = <x,x>1/2.

Refinement of

Associated types

Those defined by BanachSpace:

Notation

X A type that is a model of HilbertSpace
v,w Object of type X

Definitions

Valid expressions

In addition to those defined by BanachSpace:
Name Expression Type requirements Return type
Inner product inner_prod( v, w ) value_type

Expression semantics

Name Expression Precondition Semantics Postcondition
Inner product inner_prod( v, w )

Complexity guarantees

Invariants

Models

Notes