Welcome to our community

Be a part of something great, join today!

Can a given basis of a vector space (V,O_1,O_2) can it represent two different graphs

vs140580

New member
Dec 28, 2018
2
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 same set V can they both have same bases. (If not kind help with a proof or link of it to improve my knowledge.)


Here O_1,O_2,a_1,a_2 are operations on V.
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
371
Here O_1,O_2,a_1,a_2 are operations on V.
By "operations", do you mean that O_1 and a_1, say, are "scalar multiplication" and O_2 and a_2 are vector addition?
 

vs140580

New member
Dec 28, 2018
2
By "operations", do you mean that O_1 and a_1, say, are "scalar multiplication" and O_2 and a_2 are vector addition?

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.