# Exterior form

From Encyclopedia of Mathematics

*of degree , exterior -form*

A homogeneous element of degree of the exterior algebra of a vector space , i.e. an element of the -th exterior power . The expression "exterior form of degree r on the space V" usually denotes a skew-symmetric -linear function (or a skew-symmetric times covariant tensor) on . The direct sum of the spaces of skew-symmetric -linear functions on , endowed with the exterior product, is an algebra isomorphic to the exterior algebra .

Under an exterior form one also understands a differential form.

**How to Cite This Entry:**

Exterior form. A.L. Onishchik (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Exterior_form&oldid=12920

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098