Alternating Multilinear Form

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

 F:V tensor ... tensor V->R

such that


for any index i. For example,


is an alternating form on R^3.

An alternating multilinear form is defined on a module in a similar way, by replacing R 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 MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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