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Form Envelope


Given a differential p-form q in the exterior algebra  ^ ^pV^*, its envelope 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 k-Form, Differential Ideal, Exterior Algebra, Vector Space, Wedge Product

This entry contributed by Todd Rowland

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Cite this as:

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

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