Affine coordinate frame

A set of linearly-independent vectors () of -dimensional affine space , and a point . The point is called the initial point, while the vectors are the scale vectors. Any point is defined with respect to the affine coordinate frame by numbers — coordinates , occurring in the decomposition of the position vector by the scale vectors: (summation convention). The specification of two affine coordinate frames defines a unique affine transformation of the space which converts the first frame into the second (see also Affine coordinate system).

Comments

An equivalent, and more usual, definition is as follows. An affine coordinate frame in affine -space is a set of points which are linearly independent in the affine sense, i.e. the vectors , , are linearly independent in the corresponding vector space. Independence of the vectors in the definition should be understood as independence in a corresponding vector space.

References

[1]	E. Snapper, R.J. Troyer, "Metric affine geometry" , Acad. Press (1971)