An alternating multilinear form on a real vector space
is a multilinear form

(1)

such that

(2)

for any index . For example,

(3)

is an alternating form on .
An alternating multilinear form is defined on a module in a similar way, by replacing with the ring.
See also
Dual Vector Space,
Exterior Algebra,
Module,
Multilinear
Form,
Vector Space
This entry contributed by Todd
Rowland
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Cite this as:
Rowland, Todd. "Alternating Multilinear Form." From MathWorldA Wolfram Web Resource, created
by Eric W. Weisstein. https://mathworld.wolfram.com/AlternatingMultilinearForm.html
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