Kronecker delta
E100234
concept in discrete mathematics
concept in linear algebra
concept in tensor calculus
mathematical function
symbol
The Kronecker delta is a function of two variables that equals 1 when the variables are equal and 0 otherwise, widely used in linear algebra, tensor calculus, and discrete mathematics to represent identity relations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kronecker delta canonical | 2 |
| Kronecker delta (discrete case) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T846899 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kronecker delta Context triple: [Leopold Kronecker, notableWork, Kronecker delta]
-
A.
Christoffel symbols
Christoffel symbols are mathematical objects in differential geometry that represent how coordinate bases change from point to point on a curved space or spacetime, and are used to define covariant derivatives and geodesics.
-
B.
Kretschmann scalar
The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
-
C.
Kac
Kac is a surname most notably associated with Polish-American mathematician Mark Kac, known for his work in probability theory and mathematical physics.
-
D.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
-
E.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kronecker delta Target entity description: The Kronecker delta is a function of two variables that equals 1 when the variables are equal and 0 otherwise, widely used in linear algebra, tensor calculus, and discrete mathematics to represent identity relations.
-
A.
Christoffel symbols
Christoffel symbols are mathematical objects in differential geometry that represent how coordinate bases change from point to point on a curved space or spacetime, and are used to define covariant derivatives and geodesics.
-
B.
Kretschmann scalar
The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
-
C.
Kac
Kac is a surname most notably associated with Polish-American mathematician Mark Kac, known for his work in probability theory and mathematical physics.
-
D.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
-
E.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in discrete mathematics
ⓘ
concept in linear algebra ⓘ concept in tensor calculus ⓘ mathematical function ⓘ symbol ⓘ |
| appearsIn |
Ricci calculus
ⓘ
surface form:
Einstein summation convention
|
| category | indicator function of equality ⓘ |
| codomain | {0,1} ⓘ |
| componentOf | identity matrix entries ⓘ |
| contractionRule |
A_i δ_ij = A_j
ⓘ
δ_ij A_j = A_i ⓘ |
| definedOn | pair of indices ⓘ |
| definition | δ_ij = 1 if i = j and 0 otherwise ⓘ |
| domain | ℤ × ℤ ⓘ |
| field | mathematics ⓘ |
| generalization | multi-index Kronecker delta ⓘ |
| hasAlternativeNotation | δ(i,j) ⓘ |
| hasSymbol | δ_ij ⓘ |
| idempotentProperty | δ_ij δ_jk = δ_ik ⓘ |
| isDiscreteAnalogOf | Dirac delta function ⓘ |
| logicalInterpretation | truth value of equality between indices ⓘ |
| matrixRepresentation | identity matrix ⓘ |
| namedAfter | Leopold Kronecker ⓘ |
| orthonormalityRelation | e_i · e_j = δ_ij ⓘ |
| property |
symmetric in its indices
ⓘ
δ_ii = 1 for any index i ⓘ δ_ij = 0 for i ≠ j ⓘ |
| relatedTo | Dirac delta function ⓘ |
| represents | identity relation on a set of indices ⓘ |
| roleInEinsteinSummation | acts as identity for index substitution ⓘ |
| specialCaseOf | discrete orthogonality relation ⓘ |
| symmetry | δ_ij = δ_ji ⓘ |
| takesValue |
0 when its two arguments are not equal
ⓘ
1 when its two arguments are equal ⓘ |
| tensorRank | (0,2) tensor in index notation ⓘ |
| usedFor |
discrete convolution identities
ⓘ
encoding equality constraints between indices ⓘ selecting components in sums ⓘ simplifying tensor expressions ⓘ |
| usedIn |
discrete mathematics
ⓘ
index notation ⓘ linear algebra ⓘ quantum mechanics ⓘ representation of identity operators ⓘ summation notation ⓘ tensor analysis ⓘ Ricci calculus ⓘ
surface form:
tensor calculus
|
| usedToDefine | components of identity tensor ⓘ |
| usedToExpress | orthonormality of basis vectors ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Kronecker delta Description of subject: The Kronecker delta is a function of two variables that equals 1 when the variables are equal and 0 otherwise, widely used in linear algebra, tensor calculus, and discrete mathematics to represent identity relations.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kronecker delta (discrete case)