math::HilbertSpace< I, Vector, Scalar, N > Struct Template Reference
[Concepts]

Concept HilbertSpace. More...

#include <vector_concepts.hpp>

Inherits InnerProduct< I, Vector, Scalar >, and BanachSpace< N, Vector, Scalar >.

Collaboration diagram for math::HilbertSpace< I, Vector, Scalar, N >:

[legend]

List of all members.

Public Member Functions
axiom	Consistency (Vector v)
	Consistency between norm and induced norm.

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Detailed Description

template<typename I, typename Vector, typename Scalar = typename Vector::value_type, typename N = induced_norm_t<I, Vector, Scalar>>
struct math::HilbertSpace< I, Vector, Scalar, N >

Concept HilbertSpace.

A Hilbert space is a vector space with an inner product that induces a norm

Parameters:

	I	Inner product functor
	Vector	The the type of a vector or a collection
	Scalar	The scalar over which the vector field is defined
	N	Norm functor

Refinement of:

• InnerProduct <I, Vector, Scalar>
• BanachSpace <N, Vector, Scalar>

Note:

• The (expressible) requirements of Banach Space are already given in InnerProduct (besides consistency of the functors).
• A difference is that InnerProduct is not a refinement of Vectorspace

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Member Function Documentation

template<typename I , typename Vector , typename Scalar = typename Vector::value_type, typename N = induced_norm_t<I, Vector, Scalar>>

axiom math::HilbertSpace< I, Vector, Scalar, N >::Consistency

(

Vector

v

)

[inline]

Consistency between norm and induced norm.

math::induced_norm_t<I, Vector, Scalar>()(v) == N()(v);

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The documentation for this struct was generated from the following file:

• vector_concepts.hpp