Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Hilbert_space_l2
|
| gptkbp:application |
gptkb:signal_processing
functional analysis quantum mechanics |
| gptkbp:basisFor |
standard basis (sequences with 1 in one position, 0 elsewhere)
|
| gptkbp:complete |
true
|
| gptkbp:containsElement |
sequence (x_n) such that sum |x_n|^2 < infinity
|
| gptkbp:definedIn |
the space of all infinite sequences of real or complex numbers whose series of squares is convergent
|
| gptkbp:dimensions |
infinite
|
| gptkbp:hasDual |
itself (self-dual)
|
| https://www.w3.org/2000/01/rdf-schema#label |
sequence space l2
|
| gptkbp:innerProduct |
sum x_n * conjugate(y_n)
|
| gptkbp:isA |
gptkb:Hilbert_space
sequence space |
| gptkbp:norm |
l2 norm
|
| gptkbp:notation |
l2
|
| gptkbp:property |
orthonormal basis exists
reflexive parallelogram law holds uniformly convex |
| gptkbp:separates |
true
|
| gptkbp:bfsParent |
gptkb:Hilbert_space
|
| gptkbp:bfsLayer |
4
|