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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:Physics
Economics
Engineering
Computer science
Statistics
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gptkbp:basisFor
|
Basis
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gptkbp:containsElement
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gptkb:Vector
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gptkbp:definedIn
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gptkb:Field
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gptkbp:dimensions
|
Dimension
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gptkbp:field
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gptkb:Linear_algebra
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gptkbp:generalizes
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gptkb:Euclidean_space
gptkb:Function_space
gptkb:Polynomial_space
gptkb:Sequence_space
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gptkbp:hasAxiom
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Associativity of addition
Commutativity of addition
Existence of additive identity
Existence of additive inverse
Identity element of scalar multiplication
Compatibility of scalar multiplication with field multiplication
Distributivity of scalar multiplication with respect to field addition
Distributivity of scalar multiplication with respect to vector addition
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gptkbp:hasProperty
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gptkb:Homomorphism
gptkb:Isomorphism
gptkb:Quotient_space
Closure under addition
Direct sum
Span
Closure under scalar multiplication
Finite dimension
Infinite dimension
Linear independence
Zero vector
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https://www.w3.org/2000/01/rdf-schema#label
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Vector spaces
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gptkbp:introducedIn
|
19th century
|
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gptkbp:notablePerson
|
gptkb:David_Hilbert
gptkb:Giuseppe_Peano
gptkb:Hermann_Weyl
gptkb:Arthur_Cayley
gptkb:Hermann_Grassmann
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gptkbp:operator
|
Scalar multiplication
Vector addition
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gptkbp:relatedTo
|
gptkb:Hilbert_space
gptkb:Affine_space
gptkb:Inner_product_space
gptkb:Normed_vector_space
Module
|
|
gptkbp:studiedBy
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Mathematicians
|
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gptkbp:subunit
|
gptkb:Subspace
|
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gptkbp:bfsParent
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gptkb:Tensor_product
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gptkbp:bfsLayer
|
6
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