Gaussian elimination
E29360
Gaussian elimination is a fundamental algorithm in linear algebra used to solve systems of linear equations by systematically transforming matrices into row-echelon form.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Gaussian elimination canonical | 5 |
| Gauss–Jordan elimination | 2 |
| Gaussian elimination with full pivoting | 1 |
| Gaussian elimination with partial pivoting | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T228919 — 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: Gaussian elimination Context triple: [Carl Friedrich Gauss, notableWork, Gaussian elimination]
-
A.
Polynomial Root Finder
Polynomial Root Finder is a TI-84 Plus calculator application that computes the roots of polynomial equations quickly and accurately.
-
B.
Aitken
Aitken is a Scottish-origin surname notably borne by Max Aitken, 1st Baron Beaverbrook, a prominent Canadian-British newspaper magnate and politician.
-
C.
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.
-
D.
Euclidean space
Euclidean space is the standard flat, n-dimensional geometric setting of classical geometry and vector calculus, characterized by straight lines, right angles, and the usual distance and dot product.
-
E.
EGA
EGA is the common abbreviation for the Eagle, Globe, and Anchor emblem that symbolizes the United States Marine Corps.
- 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: Gaussian elimination Target entity description: Gaussian elimination is a fundamental algorithm in linear algebra used to solve systems of linear equations by systematically transforming matrices into row-echelon form.
-
A.
Polynomial Root Finder
Polynomial Root Finder is a TI-84 Plus calculator application that computes the roots of polynomial equations quickly and accurately.
-
B.
Aitken
Aitken is a Scottish-origin surname notably borne by Max Aitken, 1st Baron Beaverbrook, a prominent Canadian-British newspaper magnate and politician.
-
C.
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.
-
D.
Euclidean space
Euclidean space is the standard flat, n-dimensional geometric setting of classical geometry and vector calculus, characterized by straight lines, right angles, and the usual distance and dot product.
-
E.
EGA
EGA is the common abbreviation for the Eagle, Globe, and Anchor emblem that symbolizes the United States Marine Corps.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
algorithm
ⓘ
linear algebra method ⓘ matrix algorithm ⓘ |
| applicableTo |
systems with infinitely many solutions
ⓘ
systems with no solution ⓘ systems with unique solutions ⓘ |
| assumes | arithmetic operations are exact in theoretical analysis ⓘ |
| basedOn | elementary row operations ⓘ |
| canDetect |
linear dependence of rows
ⓘ
singularity of a matrix ⓘ |
| field | linear algebra ⓘ |
| historicalOrigin | methods known in ancient Chinese mathematics ⓘ |
| input |
coefficient matrix of a linear system
ⓘ
right-hand side vector of a linear system ⓘ |
| limitation | can be numerically unstable without pivoting ⓘ |
| namedAfter | Carl Friedrich Gauss ⓘ |
| numericalVariant |
Gaussian elimination
self-linksurface differs
ⓘ
surface form:
Gaussian elimination with full pivoting
Gaussian elimination self-linksurface differs ⓘ
surface form:
Gaussian elimination with partial pivoting
|
| operatesOn |
augmented matrices
ⓘ
matrices ⓘ |
| output |
row echelon form of a matrix
ⓘ
solution of a linear system ⓘ |
| property | preserves solution set of the linear system ⓘ |
| relatedTo |
Gaussian elimination
self-linksurface differs
ⓘ
surface form:
Gauss–Jordan elimination
LU decomposition ⓘ reduced row echelon form ⓘ row echelon form ⓘ |
| step |
back substitution
ⓘ
forward elimination ⓘ |
| timeComplexity | O(n^3) for an n by n system ⓘ |
| usedFor |
computing determinants
ⓘ
computing matrix rank ⓘ finding inverses of matrices ⓘ reducing matrices to reduced row echelon form ⓘ reducing matrices to row echelon form ⓘ solving systems of linear equations ⓘ |
| usedIn |
computer graphics
ⓘ
data analysis ⓘ engineering ⓘ numerical linear algebra libraries ⓘ scientific computing ⓘ |
| usesOperation |
row replacement
ⓘ
row scaling ⓘ row swapping ⓘ |
| worksOver |
complex numbers
ⓘ
fields ⓘ finite fields ⓘ real numbers ⓘ |
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: Gaussian elimination Description of subject: Gaussian elimination is a fundamental algorithm in linear algebra used to solve systems of linear equations by systematically transforming matrices into row-echelon form.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Gauss–Jordan elimination
this entity surface form:
Gaussian elimination with partial pivoting
this entity surface form:
Gaussian elimination with full pivoting
this entity surface form:
Gauss–Jordan elimination