UpperTriangular
E440648
UpperTriangular is a linear algebra type representing square matrices whose entries below the main diagonal are zero, enabling efficient storage and specialized algorithms.
All labels observed (1)
| Label | Occurrences |
|---|---|
| UpperTriangular canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4443219 — 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: UpperTriangular Context triple: [LinearAlgebra, exportsType, UpperTriangular]
-
A.
Tregami
Tregami is a Nuristani language spoken by a small community in eastern Afghanistan’s remote valleys.
-
B.
Triangle
Triangle is a small sugar-producing town in southeastern Zimbabwe known for its large sugar estates and milling operations.
-
C.
UP
UP is the standard reporting mark used to identify rail equipment owned or operated by the Union Pacific Railroad in North America.
-
D.
UP
UP is a leading South African public research university located in Pretoria, known for its comprehensive range of academic programs and strong research output.
-
E.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
- 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: UpperTriangular Target entity description: UpperTriangular is a linear algebra type representing square matrices whose entries below the main diagonal are zero, enabling efficient storage and specialized algorithms.
-
A.
Tregami
Tregami is a Nuristani language spoken by a small community in eastern Afghanistan’s remote valleys.
-
B.
Triangle
Triangle is a small sugar-producing town in southeastern Zimbabwe known for its large sugar estates and milling operations.
-
C.
UP
UP is the standard reporting mark used to identify rail equipment owned or operated by the Union Pacific Railroad in North America.
-
D.
UP
UP is a leading South African public research university located in Pretoria, known for its comprehensive range of academic programs and strong research output.
-
E.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
linear algebra data structure
ⓘ
matrix type ⓘ |
| belongsTo | category of structured matrices ⓘ |
| canBeStoredAs | compact representation of upper triangle including diagonal ⓘ |
| enables |
efficient storage
ⓘ
specialized algorithms ⓘ |
| hasAdvantage |
allows specialized kernels exploiting zero structure
ⓘ
reduces number of stored elements compared to full matrix ⓘ |
| hasConstraint |
indices below diagonal are implicitly zero
ⓘ
matrix must be square ⓘ |
| hasLowerPart | zero entries ⓘ |
| hasMainDiagonal | possibly nonzero entries ⓘ |
| hasProperty |
all nonzero entries are on or above main diagonal
ⓘ
entries below main diagonal are zero ⓘ |
| hasUpperPart | possibly nonzero entries ⓘ |
| hasUseCase |
block upper triangular systems
ⓘ
efficient repeated solves with same triangular matrix ⓘ |
| isAssumedIn | algorithms that skip operations on known zeros below diagonal ⓘ |
| isCharacterizedBy | a_ij = 0 for i > j ⓘ |
| isCommonIn |
R factor of QR factorization
ⓘ
solutions of linear systems after Gaussian elimination ⓘ upper factor of LU factorization ⓘ |
| isDefinedOver | a field or ring of matrix entries ⓘ |
| isImportantFor |
numerical stability analysis of algorithms
ⓘ
theoretical linear algebra proofs involving triangularization ⓘ |
| isRelatedTo |
Diagonal matrix
ⓘ
LowerTriangular ⓘ |
| isSubtypeOf |
square matrix type
ⓘ
triangular matrix type ⓘ |
| isUsedBy | numerical linear algebra libraries ⓘ |
| isUsedIn |
Cholesky decomposition
ⓘ
LU decomposition ⓘ QR decomposition (R factor) ⓘ factorization algorithms ⓘ |
| mayBe |
non-unit upper triangular (arbitrary diagonal)
ⓘ
unit upper triangular (ones on diagonal) ⓘ |
| optimizes |
memory usage for sparse lower part
ⓘ
time complexity of certain matrix operations ⓘ |
| represents | square matrix ⓘ |
| supportsOperation |
matrix-matrix multiplication
ⓘ
matrix-vector multiplication ⓘ solving linear systems with triangular coefficient matrix ⓘ |
| usedFor |
backward substitution
ⓘ
forward substitution ⓘ solving triangular systems ⓘ |
| usedIn | linear algebra computations ⓘ |
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: UpperTriangular Description of subject: UpperTriangular is a linear algebra type representing square matrices whose entries below the main diagonal are zero, enabling efficient storage and specialized algorithms.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.