Thank you for the reply. This has helped me quiet alot, and has changed how I plan to continue my essay.
EDIT: What i meant is definatly a tensor. The tensor you refer to is a modern definition. By tensor I mean a signless number which is a stretch factor rather than length.
I am suggesting...
By tensor I mean a positive real number which acts as a "scale factor". It simply changes the length of the vector.
A interesting point to note here is that 0 is *not* a tensor as this would change the direction, though the limit exists.
My aim is to interpret two-dimension vector quotients. I will be using this as the analogue to what a quaternion is.
Ok here goes:
*only considering vectors in two-dimensions*
We define a vector to be a directed line from A to B.
We define equality between two vectors if we can use...