SymTridiagonal
E440654
SymTridiagonal is a Julia type representing a symmetric tridiagonal matrix optimized for efficient storage and linear algebra operations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| SymTridiagonal canonical | 1 |
| SymTridiagonal(d, e) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4443262 — 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: SymTridiagonal Context triple: [SparseArrays, definesType, SymTridiagonal]
-
A.
Jacobi method
The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
-
B.
Jacobi
Jacobi is a German surname most famously associated with the 19th-century mathematician Carl Gustav Jacob Jacobi, known for his foundational work in elliptic functions and number theory.
-
C.
Jacobi operator
The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
-
D.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
-
E.
Schmidt orthogonalization
Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
- 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: SymTridiagonal Target entity description: SymTridiagonal is a Julia type representing a symmetric tridiagonal matrix optimized for efficient storage and linear algebra operations.
-
A.
Jacobi method
The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
-
B.
Jacobi
Jacobi is a German surname most famously associated with the 19th-century mathematician Carl Gustav Jacob Jacobi, known for his foundational work in elliptic functions and number theory.
-
C.
Jacobi operator
The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
-
D.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
-
E.
Schmidt orthogonalization
Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
JuliaType
ⓘ
MatrixType ⓘ |
| assumes | symmetryFromTridiagonalData ⓘ |
| belongsToModule | LinearAlgebra ⓘ |
| commonEltype |
ComplexF64
ⓘ
Float32 ⓘ Float64 ⓘ |
| compatibleWith |
BLAS
ⓘ
LAPACK ⓘ |
| constructorArgument |
diagonalVector_d
ⓘ
offDiagonalVector_e ⓘ |
| definedIn |
JuliaLanguage
ⓘ
linked to:
Julia
|
| diagonalCount | 3 ⓘ |
| elementType | Number ⓘ |
| hasConstructor |
SymTridiagonal(d, e)
ⓘ
linked to:
SymTridiagonal
|
| hasMethod |
*(::SymTridiagonal, ::AbstractMatrix)
ⓘ
*(::SymTridiagonal, ::AbstractVector) ⓘ cholesky(::SymTridiagonal) ⓘ eigen(::SymTridiagonal) ⓘ eigvals(::SymTridiagonal) ⓘ eigvecs(::SymTridiagonal) ⓘ getindex(::SymTridiagonal, ::Int, ::Int) ⓘ ldlt(::SymTridiagonal) ⓘ setindex!(::SymTridiagonal, ::Number, ::Int, ::Int) ⓘ size(::SymTridiagonal) ⓘ |
| hasProperty |
symmetric
ⓘ
tridiagonal ⓘ |
| isSubtypeOf | AbstractMatrix ⓘ |
| matrixShape | square ⓘ |
| optimizedFor |
efficientStorage
ⓘ
linearAlgebraOperations ⓘ |
| providedBy |
LinearAlgebra.jl
ⓘ
linked to:
LinearAlgebra
|
| storagePattern | compressedRepresentation ⓘ |
| stores |
firstSubSuperDiagonal
ⓘ
mainDiagonal ⓘ |
| supportsOperation |
eigenvalueComputation
ⓘ
factorization ⓘ linearSystemSolve ⓘ matrixMatrixMultiplication ⓘ matrixVectorMultiplication ⓘ |
| symmetryType | HermitianForComplexEltype ⓘ |
| timeComplexity |
O(n)MatrixVectorMultiply
ⓘ
O(n)Storage ⓘ |
| usedFor | symmetricTridiagonalMatrices ⓘ |
| usedIn |
eigenvalueAlgorithms
ⓘ
numericalLinearAlgebra ⓘ scientificComputing ⓘ |
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: SymTridiagonal Description of subject: SymTridiagonal is a Julia type representing a symmetric tridiagonal matrix optimized for efficient storage and linear algebra operations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: SymTridiagonal