The sum of two vector spaces $~$U$~$ and $~$W,$~$ written $~$U + W,$~$ is a vector space where the set of vectors is all possible $~$u + w$~$ for every $~$u \in U$~$ and $~$w \in W.$~$
https://arbital.com/p/vector_space_sum
by Nate Soares May 27 2016
The sum of two vector spaces $~$U$~$ and $~$W,$~$ written $~$U + W,$~$ is a vector space where the set of vectors is all possible $~$u + w$~$ for every $~$u \in U$~$ and $~$w \in W.$~$