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

BanachSpace.

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

v.norm() = <v,v>^1/2;

Models

euclidean_space< vector >.