Let K {\displaystyle {}K} be a field, and let V 1 , … , V n {\displaystyle {}V_{1},\ldots ,V_{n}} vector spaces over K {\displaystyle {}K} . Let
( i = 1 , … , n {\displaystyle {}i=1,\ldots ,n} ), denote linear mappings. Show that the mapping
is multilinear.