View source for Exterior form

<!--
e0371002.png
$#A+1 = 14 n = 0
$#C+1 = 14 : ~/encyclopedia/old_files/data/E037/E.0307100 Exterior form
Automatically converted into TeX, above some diagnostics.
Please remove this comment and the {{TEX|auto}} line below,
if TeX found to be correct.
-->

{{TEX|auto}}
{{TEX|done}}

''of degree  $  r $, 
exterior  $  r $-
form''

A homogeneous element of degree  $  r $
of the [[Exterior algebra|exterior algebra]]  $  \wedge V $
of a vector space  $  V $, 
i.e. an element of the  $  r $-
th exterior power  $  \wedge  ^ {r} V $. 
The expression  "exterior form of degree r on the space V"  usually denotes a skew-symmetric  $  r $-
linear function (or a skew-symmetric  $  r $
times covariant tensor) on  $  V $. 
The direct sum of the spaces of skew-symmetric  $  r $-
linear functions on  $  V $, 
$  r = 0, 1 \dots $
endowed with the [[Exterior product|exterior product]], is an algebra isomorphic to the exterior algebra  $  \wedge V  ^ {*} $.

Under an exterior form one also understands a [[Differential form|differential form]].