Linear subspaces/Sum/Definition

Sum of linear subspaces

For a ${}K$-vector space ${}V$ and a family of linear subspaces ${}U_{1},\ldots ,U_{n}\subseteq V$, we define the sum of these linear subspaces by

${}U_{1}+\cdots +U_{n}={\left\{u_{1}+\cdots +u_{n}\mid u_{i}\in U_{i}\right\}}\,.$