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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 >:

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List of all members.

Public Member Functions

axiom Consistency (Vector v)
 Consistency between norm and induced norm.


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:
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

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);


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


math::HilbertSpace< I, Vector, Scalar, N > Struct Template Reference -- MTL 4 -- Peter Gottschling and Andrew Lumsdaine -- Gen. with rev. 7542 on 7 Apr 2011 by doxygen 1.5.9 -- © 2010 by SimuNova UG.