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gptkbp:instanceOf
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gptkb:Vector
gptkb:mathematical_concept
gptkb:topology
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gptkbp:basisFor
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gptkb:Orthonormal_basis
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gptkbp:dimensions
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finite or infinite
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gptkbp:example
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gptkb:Euclidean_space
gptkb:L2_space
l2 sequence space
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gptkbp:generalizes
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gptkb:Euclidean_space
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gptkbp:hasApplication
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gptkb:Probability_theory
gptkb:Control_theory
Information theory
Statistics
Numerical analysis
Machine learning
Mathematical physics
Quantum computing
Operator theory
Wavelet analysis
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gptkbp:hasAxiom
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gptkb:Cauchy-Schwarz_inequality
gptkb:Triangle_inequality
Linearity
Completeness
Conjugate symmetry
Inner product space axioms
Positive-definiteness
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gptkbp:hasDualSpace
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Itself (isomorphic)
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gptkbp:hasInnerProduct
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Yes
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gptkbp:hasNorm
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Induced by inner product
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gptkbp:hasSpecialCase
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gptkb:Hilbert_space
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https://www.w3.org/2000/01/rdf-schema#label
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Hilbert Space
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gptkbp:includesMetric
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Induced by norm
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gptkbp:namedAfter
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gptkb:David_Hilbert
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gptkbp:numberOfIssues
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Yes
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gptkbp:property
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gptkb:Hilbert_space
gptkb:Riesz_representation_theorem
gptkb:Parallelogram_law
Reflexivity
Orthonormality
Projection theorem
Separability
Spectral theorem
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gptkbp:usedIn
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gptkb:signal_processing
gptkb:Quantum_mechanics
Fourier analysis
Functional analysis
Partial differential equations
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gptkbp:bfsParent
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gptkb:C*-algebra
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gptkbp:bfsLayer
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5
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