Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
gptkb:group_of_people |
| gptkbp:actsOn |
R^n
|
| gptkbp:alsoKnownAs |
general affine group
|
| gptkbp:contains |
linear transformations of R^n
translations of R^n |
| gptkbp:dimensions |
n^2 + n
|
| gptkbp:field |
R
|
| gptkbp:form |
x ↦ Ax + b, with A in GL(n, R), b in R^n
|
| gptkbp:hasSubgroup |
group of bijections of R^n
|
| https://www.w3.org/2000/01/rdf-schema#label |
affine group of R^n
|
| gptkbp:identityElement |
identity map
|
| gptkbp:isFinite |
true
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:isNonAbelian |
true
|
| gptkbp:isSemidirectProductOf |
gptkb:GL(n,_R)
R^n |
| gptkbp:notation |
GA(n, R)
|
| gptkbp:preserves |
affine structure of R^n
|
| gptkbp:relatedTo |
gptkb:Euclidean_group
projective group |
| gptkbp:bfsParent |
gptkb:Isometry_group_of_R^n
|
| gptkbp:bfsLayer |
8
|