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Form Envelope


The form envelope of a differential p-form q in the exterior algebra  ^ ^pV^* is the smallest subspace W such that q is in the subspace  ^ ^pW^* subset  ^ ^pV^*. Alternatively, W is spanned by the vectors that can be written as the tensor contraction of q with an element of  ^ ^(p-1)V.

For example, the envelope of dx in V=R^2 is W=<partial/partialx>, and the envelope of dx_1 ^ dx_2+dx_3 ^ dx_4 in V=R^4 is all of V.


See also

Decomposable, Differential Ideal, Differential k-Form, Exterior Algebra, Vector Space, Wedge Product

This entry contributed by Todd Rowland

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Cite this as:

Weisstein, Eric W., with contributions by Todd Rowland. "Form Envelope." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FormEnvelope.html

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