Top-Dimensional Form
In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then
| alpha=e_1 ^ e_2 ^ e_3 ^ e_4 |
is a top-dimensional form, and any other top-dimensional form is lambdaalpha for some lambda.
See also
Differential k-Form, Exterior Algebra, Vector Space OrientationThis entry contributed by Todd Rowland
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Cite this as:
Rowland, Todd. "Top-Dimensional Form." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Top-DimensionalForm.html