Exterior Algebra
The Algebra of the Exterior Product, also called an Alternating Algebra or Grassmann Algebra. Thestudy of exterior algebra is also called Ausdehnungslehre and Extensions Calculus. Exterior algebras areGraded Algebras.
In particular, the exterior algebra of a Vector Space is the Direct Sum over 
in thenatural numbers of the Vector Spaces of alternating -forms on that Vector Space. The producton this algebra is then the wedge product of forms. The exterior algebra for a Vector Space 
is constructed byforming monomials 
, 
, 
, etc., where , 
, 
, 
, 
, and 
are vectors in and
is asymmetric multiplication. The sums formed from linear combinations of the Monomials are theelements of an exterior algebra.
References
Forder, H. G. The Calculus of Extension. Cambridge, England: Cambridge University Press, 1941. Lounesto, P. ``Counterexamples to Theorems Published and Proved in Recent Literature on Clifford Algebras, Spinors, Spin Groups, and the Exterior Algebra.'' http://www.hit.fi/~lounesto/counterexamples.htm.
- Pullback Map
- Pulse Function
- Purser's Theorem
- Pursuit Curve
- Push
- Puzzle
- P-Value
- Pyramid
- Pyramidal Frustum
- Pyramidal Number
- Pyritohedron
- Pythagoras's Constant
- Pythagoras's Theorem
- Pythagoras Tree
- Pythagorean Fraction
- Pythagorean Quadruple
- Pythagorean Square Puzzle
- Pythagorean Theorem
- Pythagorean Triad
- Pythagorean Triangle
- Pythagorean Triple
- Pépin's Test
- Pépin's Theorem
- Pólya-Burnside Lemma
- Pólya Conjecture