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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:alsoKnownAs
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dot product
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gptkbp:application
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gptkb:machine_learning
computer science
engineering
physics
statistics
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gptkbp:definedIn
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gptkb:Euclidean_space
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gptkbp:dimensions
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finite-dimensional vector spaces
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gptkbp:field
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gptkb:geometry
linear algebra
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gptkbp:form
|
sum of products of corresponding components
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gptkbp:generalizes
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scalar product
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gptkbp:hasSpecialCase
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gptkb:inner_product
|
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gptkbp:introduced
|
gptkb:Euclid
|
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gptkbp:isBilinear
|
true
|
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gptkbp:isPositiveDefinite
|
true
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gptkbp:mapType
|
pair of vectors to a scalar
|
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gptkbp:notation
|
x · y
⟨x, y⟩
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gptkbp:property
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⟨ax+by, z⟩ = a⟨x, z⟩ + b⟨y, z⟩
⟨x, x⟩ = 0 iff x = 0
⟨x, x⟩ ≥ 0
⟨x, y⟩ = ⟨y, x⟩
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gptkbp:relatedTo
|
gptkb:Cauchy-Schwarz_inequality
gptkb:standard
gptkb:Gram-Schmidt_process
gptkb:Pythagorean_theorem
orthonormal basis
orthogonal projection
angle formula
|
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gptkbp:symmetry
|
true
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gptkbp:usedFor
|
orthogonality
measuring angle between vectors
measuring length of vectors
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gptkbp:bfsParent
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gptkb:SO(n)
gptkb:orthogonal_group_O(n)
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gptkbp:bfsLayer
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7
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|
https://www.w3.org/2000/01/rdf-schema#label
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Euclidean inner product
|