Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Vector
gptkb:mathematical_concept inner product space |
| gptkbp:example |
gptkb:L2_space
l2 space finite-dimensional real vector space finite-dimensional complex vector space |
| gptkbp:generalizes |
gptkb:Euclidean_space
|
| gptkbp:hasAxiom |
gptkb:parallelogram_law
|
| gptkbp:hasProperty |
gptkb:Hilbert_space
bounded linear operators compact operators direct sum decomposition orthogonal complement unitary operators complete complete metric space orthonormal basis exists reflexive metric induced by norm self-dual inner product induces norm norm induced by inner product parallelogram law holds Bessel's inequality holds Hilbert dimension Parseval's identity holds Pythagorean theorem holds Riesz representation theorem holds dual space isomorphic to itself finite-dimensional possible infinite-dimensional possible orthogonality defined projection theorem holds separable (sometimes) separable if countable orthonormal basis spectral theorem applies |
| https://www.w3.org/2000/01/rdf-schema#label |
espaces de Hilbert
|
| gptkbp:namedAfter |
gptkb:David_Hilbert
|
| gptkbp:operator |
gptkb:Gram-Schmidt_process
orthonormal basis orthogonal projection tensor product direct sum |
| gptkbp:structure |
inner product
|
| gptkbp:usedIn |
gptkb:signal_processing
Fourier analysis functional analysis quantum mechanics |
| gptkbp:bfsParent |
gptkb:formalisme_de_Dirac
|
| gptkbp:bfsLayer |
8
|