general linear group GL(n,R)
E593509
The general linear group GL(n,ℝ) is the Lie group consisting of all invertible n×n real matrices under matrix multiplication, fundamental in linear algebra and differential geometry.
All labels observed (7)
| Label | Occurrences |
|---|---|
| GL(n,ℝ) | 6 |
| GL(n,R) | 4 |
| general linear group | 2 |
| GL(n+1,R) | 1 |
| algebraic group GL_n over ℝ | 1 |
| general linear group GL(n+3,ℝ) | 1 |
| general linear group GL(n,R) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6456476 — 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: general linear group GL(n,R) Context triple: [Lie group, hasExample, general linear group GL(n,R)]
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A.
affine group of R^n
The affine group of ℝⁿ is the group of all invertible affine transformations of n-dimensional real space, combining linear transformations with translations.
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B.
special orthogonal group SO(n)
The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
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C.
orthogonal group O(n)
The orthogonal group O(n) is the group of all n×n real matrices that preserve the standard Euclidean inner product, representing rotations and reflections in n-dimensional space.
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D.
Lie group
A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
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E.
Euclidean group
The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
- 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: general linear group GL(n,R) Target entity description: The general linear group GL(n,ℝ) is the Lie group consisting of all invertible n×n real matrices under matrix multiplication, fundamental in linear algebra and differential geometry.
-
A.
affine group of R^n
The affine group of ℝⁿ is the group of all invertible affine transformations of n-dimensional real space, combining linear transformations with translations.
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B.
special orthogonal group SO(n)
The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
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C.
orthogonal group O(n)
The orthogonal group O(n) is the group of all n×n real matrices that preserve the standard Euclidean inner product, representing rotations and reflections in n-dimensional space.
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D.
Lie group
A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
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E.
Euclidean group
The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
- F. None of above. chosen
Statements (48)
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: general linear group GL(n,R) Description of subject: The general linear group GL(n,ℝ) is the Lie group consisting of all invertible n×n real matrices under matrix multiplication, fundamental in linear algebra and differential geometry.
Referenced by (16)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: general linear group GL(n,R)
linked to: general linear group GL(n,R)
linked to: general linear group GL(n,R)
linked to: general linear group GL(n,R)
linked to: general linear group GL(n,R)
linked to: general linear group GL(n,R)
linked to: general linear group GL(n,R)
subject linked to:
special orthogonal group SO(n)
linked to: general linear group GL(n,R)
subject linked to:
special orthogonal group SO(n)
linked to: general linear group GL(n,R)
linked to: general linear group GL(n,R)
subject linked to:
general linear group GL(n,R)
linked to: general linear group GL(n,R)
subject linked to:
special linear group SL(n,R)
linked to: general linear group GL(n,R)
subject linked to:
special linear group SL(n,R)
linked to: general linear group GL(n,R)
subject linked to:
special linear group SL(n,R)
linked to: general linear group GL(n,R)
subject linked to:
special linear group SL(n,R)
linked to: general linear group GL(n,R)