Summary: Alternating and symmetric multilinear functions.
Suppose V and W are normed vector spaces.
Definition. For each integer p we set
p
(V ; W) =



{0} if p < 0;
W if p = 0;
L(V . . . · · · . . . V
p times
; W) if p 1.
We say µ
p
(V ; W) is symmetric if either p 1 or p > 1 and the value of µ does not change if any
pair of its arguments are transposed, and we say µ is antisymmetric or alternating if either p 1 or the
value of µ is multiplied by -1 if any pair its arguments are transposed. We let
p
(V ; W) and

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics