Exterior form

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.