TOPICS
Search

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 Orientation, Volume Form

This entry contributed by Todd Rowland

Explore with Wolfram|Alpha

Cite this as:

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

Subject classifications