A subspace $~$U=(F_U, V_U)$~$ of a Vector space $~$W=(F_W, V_W)$~$ is a vector space where $~$F_U = F_W$~$ and $~$V_U$~$ is a Subgroup of $~$V_W,$~$ and $~$V_U$~$ is [ closed] under scalar multiplication.
https://arbital.com/p/vector_subspace
by Nate Soares May 27 2016
A subspace $~$U=(F_U, V_U)$~$ of a Vector space $~$W=(F_W, V_W)$~$ is a vector space where $~$F_U = F_W$~$ and $~$V_U$~$ is a Subgroup of $~$V_W,$~$ and $~$V_U$~$ is [ closed] under scalar multiplication.