Is there a paper or book that has rigorously constructed the space of "arrow vectors" and shown that it is a vector space?
By "arrow vectors" I mean oriented line segments in Euclidean n-space. This space will be over the field of real numbers and the operations of vector addition and scalar multiplication are defined as usual:
- Vector Addition is defined via the parallelogram method
- Scalar multiplication is defined by scaling a line segment by the amount of the scalar. Where multiplication by positive numbers preserves direction and negative numbers reverses it.
I'm just wondering how far anyone has followed the heuristic.