ISO(n)
E518472
ISO(n) is the n-dimensional Euclidean group consisting of all distance-preserving transformations—combinations of rotations, reflections, and translations—of n-dimensional Euclidean space.
All labels observed (1)
| Label | Occurrences |
|---|---|
| ISO(n) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5425598 — 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: ISO(n) Context triple: [Euclidean group, hasNotation, ISO(n)]
-
A.
ISOO
ISOO is a U.S. government office responsible for overseeing the security classification system and safeguarding of national security information.
-
B.
ISoN
ISoN is the commonly used abbreviation for the Ingram School of Nursing, an academic institution focused on nursing education and research.
-
C.
ISO 3297
ISO 3297 is the international standard that defines the structure, assignment, and use of the International Standard Serial Number (ISSN) for identifying serial publications.
-
D.
ISO 23950
ISO 23950 is an international standard that defines the Z39.50 client-server protocol for searching and retrieving information from remote databases in a networked environment.
-
E.
ISO standards
ISO standards are internationally agreed-upon specifications and guidelines developed by the International Organization for Standardization to ensure quality, safety, efficiency, and interoperability across products, services, and systems.
- 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: ISO(n) Target entity description: ISO(n) is the n-dimensional Euclidean group consisting of all distance-preserving transformations—combinations of rotations, reflections, and translations—of n-dimensional Euclidean space.
-
A.
ISOO
ISOO is a U.S. government office responsible for overseeing the security classification system and safeguarding of national security information.
-
B.
ISoN
ISoN is the commonly used abbreviation for the Ingram School of Nursing, an academic institution focused on nursing education and research.
-
C.
ISO 3297
ISO 3297 is the international standard that defines the structure, assignment, and use of the International Standard Serial Number (ISSN) for identifying serial publications.
-
D.
ISO 23950
ISO 23950 is an international standard that defines the Z39.50 client-server protocol for searching and retrieving information from remote databases in a networked environment.
-
E.
ISO standards
ISO standards are internationally agreed-upon specifications and guidelines developed by the International Organization for Standardization to ensure quality, safety, efficiency, and interoperability across products, services, and systems.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical group
ⓘ
matrix group ⓘ topological group ⓘ |
| actionType | isometric action ⓘ |
| actsOn |
R^n
ⓘ
n-dimensional Euclidean space ⓘ |
| applicationArea |
classical mechanics
ⓘ
computer vision ⓘ crystallography ⓘ rigid body mechanics ⓘ robotics ⓘ |
| componentGroup |
O(n)/SO(n)
ⓘ
linked to:
orthogonal group O(n)
|
| connectedComponentOfIdentity | SO(n) ⋉ R^n ⓘ |
| containsTransformations |
reflections
ⓘ
rotations ⓘ translations ⓘ |
| dimension | n(n+1)/2 ⓘ |
| elementType |
combination of reflection and translation
ⓘ
combination of rotation and translation ⓘ distance-preserving transformation ⓘ isometry of R^n ⓘ |
| field | mathematics ⓘ |
| groupOperation | composition of maps ⓘ |
| hasSubgroup |
E(n)
ⓘ
SO(n) ⓘ orientation-preserving Euclidean group ⓘ |
| isometryGroupOf |
Euclidean n-space
ⓘ
linked to:
Euclidean space
|
| isomorphicTo | O(n) ⋉ R^n ⓘ |
| normalSubgroup | R^n ⓘ |
| notationVariant |
E(n)
ⓘ
Isom(R^n) ⓘ
linked to:
Euclidean group
|
| preserves |
Euclidean distance
ⓘ
inner product up to translation ⓘ orientation (for orientation-preserving subgroup) ⓘ |
| quotientBy | R^n ⓘ |
| quotientIsomorphicTo | O(n) ⓘ |
| relatedConcept |
Euclidean geometry
ⓘ
Killing vector field on Euclidean space ⓘ rigid motion ⓘ |
| semidirectProductOf |
O(n)
ⓘ
R^n ⓘ |
| structure |
non-compact Lie group
ⓘ
non-semisimple Lie group ⓘ non-simple Lie group ⓘ |
| subfield |
Lie theory
ⓘ
geometry ⓘ group theory ⓘ |
| topology | Lie group topology induced from O(n) × R^n ⓘ |
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: ISO(n) Description of subject: ISO(n) is the n-dimensional Euclidean group consisting of all distance-preserving transformations—combinations of rotations, reflections, and translations—of n-dimensional Euclidean space.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.