Queries, comments, suggestions? Please contact us.



Area Mathematics - General concepts and linear algebra / Vectors and tensors

IEV ref102-03-02

en
point space
affine space
for a given vector space, set of elements called points, for which an element U AB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGbbGaaeOqaaWcbeaaaaa@3CB9@ of the vector space is associated to any ordered pair of points A and B with the following properties:

  • for any two points A and B, U BA = U AB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGcbGaaeyqaaWcbeaakiabg2da9iabgkHiTiaaykW7caWH vbWaaSbaaSqaaKqzGdGaaeyqaiaabkeaaSqabaaaaa@442D@ ,
  • for any three points A, B and C, U AB + U BC = U AC MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGbbGaaeOqaaWcbeaakiabgUcaRiaahwfadaWgaaWcbaqc LboacaqGcbGaae4qaaWcbeaakiabg2da9iaahwfadaWgaaWcbaqcLb oacaqGbbGaae4qaaWcbeaaaaa@4690@ ,
  • for a given point O and a given vector r, there is a unique point P such that U OP =r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGpbGaaeiuaaWcbeaakiabg2da9iaahkhaaaa@3EE0@

Note 1 to entry: A point space and the associated vector space have the same dimension. The point space derived from the three-dimensional Euclidean vector space is a model of the usual geometrical three-dimensional space.


fr
espace affine, m
espace ponctuel, m
pour un espace vectoriel donné, ensemble d'éléments appelés points, pour lesquels un élément U AB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGbbGaaeOqaaWcbeaaaaa@3CB9@ de l'espace vectoriel est associé à tout couple ordonné de points A et B avec les propriétés suivantes:

  • pour tout couple de points A et B, U BA = U AB MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGcbGaaeyqaaWcbeaakiabg2da9iabgkHiTiaaykW7caWH vbWaaSbaaSqaaKqzGdGaaeyqaiaabkeaaSqabaaaaa@442D@ ,
  • pour tout ensemble de trois points A, B et C, U AB + U BC = U AC MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGbbGaaeOqaaWcbeaakiabgUcaRiaahwfadaWgaaWcbaqc LboacaqGcbGaae4qaaWcbeaakiabg2da9iaahwfadaWgaaWcbaqcLb oacaqGbbGaae4qaaWcbeaaaaa@4690@ ,
  • pour un point donné O et un vecteur donné r, il existe un point unique P tel que U OP =r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaahwfadaWgaaWcba qcLboacaqGpbGaaeiuaaWcbeaakiabg2da9iaahkhaaaa@3EE0@

Note 1 à l'article: Un espace affine et l'espace vectoriel associé ont la même dimension. L'espace affine dérivé de l'espace vectoriel euclidien à trois dimensions est un modèle de l'espace géométrique usuel à trois dimensions.


de
affiner Punktraum, m

es
espacio afín
espacio puntual

ja
点空間
アフィン空間

pl
przestrzeń punktowa
przestrzeń afiniczna

pt
espaço pontual

sr
простор тачака, м јд
афини простор, м јд

sv
punktrymd

zh
点空间
仿射空间

Publication date: 2008-08
Copyright © IEC 2017. All Rights Reserved.