I mean the same same but the scalar multiplication and vector addition may yes but they be defined anyway may not always be the usual way.
O_1 is vector addition and O_2 scalar multiplication of first.a_1 is vector addition and a_2 scalar multiplication of second.
On the same set V.
Given a basis of a vector space $(V,O_1,O_2)$ can it represent two different non-isomorphic graphs.Any other inputs kind help. It will improve my knowledge way of my thinking.
Another kind help with this question is suppose (V,O_1,O_2) and (V,a_1,a_2) are two different vector spaces on the...