Canonical Affine Structure of a Vector Space

up:: Vector Space

Let be a vector space over a Field .

Then there is a canonical way of creating an Affine Space from it:

• Let the space’ set be the set
• Let its underlying vector space be
• Let the Group Action be the additive group

Thus, every vector space can be seen as an affine space over its own set , acted upon by its own additive group .

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References

• Basics of Affine Geometry