Let K {\displaystyle {}K} be a field, and let V 1 , … , V n , W 1 , … , W n {\displaystyle {}V_{1},\ldots ,V_{n},W_{1},\ldots ,W_{n}} and Z {\displaystyle {}Z} be vector spaces over K {\displaystyle {}K} . Let
denote linear mappings, and let
be a multilinear mapping. Show that the mapping
is also multilinear.