Let V {\displaystyle {}V} be a K {\displaystyle {}K} -vector space, let v 1 , … , v n {\displaystyle {}v_{1},\ldots ,v_{n}} be a basis of V {\displaystyle {}V} , and let
be the corresponding bijective mapping in the sense of remark. Show that this mapping transforms the componentwise addition in K n {\displaystyle {}K^{n}} into the vector addition in V {\displaystyle {}V} , that is,
holds.