Let U be a vector space, U x U the product vector space, and
# = { (u,u)|u in U} ⊆ U U.
Prove that # is a subspace of U x U and that (U x U) / # (isomorphism) U.
plx help....
What about the obvious choice of u_1,u_2)\to u_1-u_2" alt="T:U\boxplus U\to Uu_1,u_2)\to u_1-u_2" />. This is evidently surjective since and it's a homomorphism since . I claim that we are now finished. Why?
What about the obvious choice of u_1,u_2)\to u_1-u_2" alt="T:U\boxplus U\to Uu_1,u_2)\to u_1-u_2" />. This is evidently surjective since and it's a homomorphism since . I claim that we are now finished. Why?
why we only prove that # is a subspace of U then it is homomorphism
and I don't reli get why This is evidently surjective since