math::HilbertSpace< I, Vector, Scalar, N > Struct Template Reference
[Concepts]
Concept HilbertSpace.
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#include <vector_concepts.hpp>
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>>
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: