Bidiagonal
E440653
Bidiagonal is a special kind of sparse matrix that has nonzero entries only on the main diagonal and either the superdiagonal or subdiagonal, making it efficient for numerical linear algebra computations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bidiagonal canonical | 1 |
| Golub–Kahan bidiagonalization | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4443260 — 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: Bidiagonal Context triple: [SparseArrays, definesType, Bidiagonal]
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A.
Binarowa
Binarowa is a village in southern Poland known for its historic wooden architecture and cultural heritage, including the UNESCO-listed St. Michael the Archangel Church.
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B.
BDF
The BDF is the national military organization of the Kingdom of Bahrain, responsible for the country's defense and security.
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C.
BIF
BIF is the National Rail station code for Barrow-in-Furness railway station in Cumbria, England.
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D.
Bilayn
Bilayn is an alternative name for Bilen, likely referring to the same person, place, or entity under a different spelling or transliteration.
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E.
Betti
Betti is a German diminutive given name, commonly used as a short form of Bettina.
- 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: Bidiagonal Target entity description: Bidiagonal is a special kind of sparse matrix that has nonzero entries only on the main diagonal and either the superdiagonal or subdiagonal, making it efficient for numerical linear algebra computations.
-
A.
Binarowa
Binarowa is a village in southern Poland known for its historic wooden architecture and cultural heritage, including the UNESCO-listed St. Michael the Archangel Church.
-
B.
BDF
The BDF is the national military organization of the Kingdom of Bahrain, responsible for the country's defense and security.
-
C.
BIF
BIF is the National Rail station code for Barrow-in-Furness railway station in Cumbria, England.
-
D.
Bilayn
Bilayn is an alternative name for Bilen, likely referring to the same person, place, or entity under a different spelling or transliteration.
-
E.
Betti
Betti is a German diminutive given name, commonly used as a short form of Bettina.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
Bidiagonal matrix
ⓘ
Bidiagonal matrix ⓘ Matrix type ⓘ Sparse matrix ⓘ |
| belongsTo | Linear algebra ⓘ |
| enables |
Fast matrix–vector multiplication
ⓘ
Reduced storage requirements ⓘ |
| hasApplicationIn |
Computational physics
ⓘ
Data analysis ⓘ Numerical analysis ⓘ Scientific computing ⓘ |
| hasComplexityForMatVec | O(n) ⓘ |
| hasNonzeroEntriesOn |
Main diagonal
ⓘ
Subdiagonal ⓘ Superdiagonal ⓘ Superdiagonal or subdiagonal ⓘ |
| hasProperty |
At most two nonzero diagonals
ⓘ
Band matrix with bandwidth 1 ⓘ Structured sparsity pattern ⓘ |
| hasStorageComplexity | O(n) ⓘ |
| hasVariant |
Lower bidiagonal matrix
ⓘ
Upper bidiagonal matrix ⓘ |
| isCharacterizedBy | Nonzeros confined to two adjacent diagonals ⓘ |
| isContrastedWith |
Dense matrix
ⓘ
Diagonal matrix ⓘ Tridiagonal matrix ⓘ |
| isDefinedOver | Real numbers or complex numbers ⓘ |
| isObtainedBy | Bidiagonalization process ⓘ |
| isObtainedFrom | General matrix ⓘ |
| isSpecialCaseOf |
Band matrix
ⓘ
Sparse matrix ⓘ Tridiagonal matrix ⓘ |
| isUsedFor |
Efficient matrix computations
ⓘ
Eigenvalue algorithms ⓘ Singular value decomposition NERFINISHED ⓘ |
| isUsedIn |
Golub–Kahan SVD algorithm
NERFINISHED
ⓘ
Iterative methods for linear systems ⓘ Least squares computations ⓘ Numerical linear algebra ⓘ Orthogonal transformations ⓘ QR algorithm ⓘ |
| isUsedWith |
Givens rotations
NERFINISHED
ⓘ
Householder reflections NERFINISHED ⓘ |
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: Bidiagonal Description of subject: Bidiagonal is a special kind of sparse matrix that has nonzero entries only on the main diagonal and either the superdiagonal or subdiagonal, making it efficient for numerical linear algebra computations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Golub–Kahan bidiagonalization