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IEVref:102-03-02ID:
Language:enStatus: Standard
Term: point space
Synonym1: affine space
Synonym2:
Synonym3:
Symbol:
Definition: 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.


Publication date:2008-08
Source:
Replaces:
Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
CO remarks:
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