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gptkbp:instanceOf
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Mathematical structure
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gptkbp:alsoKnownAs
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gptkb:pre-Hilbert_space
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gptkbp:definedIn
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gptkb:Field
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gptkbp:dimensions
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Finite-dimensional
Infinite-dimensional
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gptkbp:enables
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gptkb:Cauchy-Schwarz_inequality
gptkb:Gram-Schmidt_process
gptkb:Pythagorean_theorem
gptkb:Parallelogram_law
gptkb:Norm
gptkb:Orthonormal_basis
Angle
Projection
Distance
Orthogonality
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gptkbp:example
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gptkb:Euclidean_space
Complex vector space with Hermitian inner product
Function space L^2
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gptkbp:field
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gptkb:Linear_algebra
Functional analysis
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gptkbp:generalizes
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gptkb:Euclidean_space
dot product
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gptkbp:hasAxiom
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Conjugate symmetry
Positive-definiteness
Linearity in first argument
Sesquilinearity
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gptkbp:hasProperty
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Orthogonality
Separability
Complete if and only if Hilbert space
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gptkbp:hasSpecialCase
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gptkb:Vector
gptkb:Normed_vector_space
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https://www.w3.org/2000/01/rdf-schema#label
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Inner product space
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gptkbp:operator
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Inner product
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gptkbp:relatedTo
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gptkb:Riesz_representation_theorem
Bessel's inequality
Unitary operator
Parseval's identity
Projection theorem
Spectral theorem
Orthogonal complement
Self-adjoint operator
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gptkbp:specialty
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gptkb:Hilbert_space
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gptkbp:usedIn
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gptkb:geometry
gptkb:signal_processing
gptkb:Quantum_mechanics
Fourier analysis
Statistics
Machine learning
Optimization
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gptkbp:bfsParent
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gptkb:Euclidean_Space
gptkb:Vector_spaces
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gptkbp:bfsLayer
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7
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