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Alternating and symmetric multilinear functions. Suppose V and W are normed vector spaces.
 

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
p
(V ; W) is symmetric if either p 1 or p > 1 and the value of does not change if any
pair of its arguments are transposed, and we say is antisymmetric or alternating if either p 1 or the
value of 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