A blade is a term often used to describe a basis entity in the space defined by a geometric algebra. Since a geometric algebra is a multi-graded space, the basis entities also have multiple grades. To distinguish the various graded entities, the blades are often prefixed by their grade. For example a grade- basis entity would be called a -blade.
The number of linearly independent -blades in a particular geometric algebra is dependent on the number of dimensions of the manifold on which the algebra is defined. For an -dimensional manifold, the number of -blades is given by the binomial coefficient.
The total number of basis blades of all grades in a geometric algebra defined on an -manifold is then:
|Date of creation||2013-03-22 15:58:40|
|Last modified on||2013-03-22 15:58:40|
|Last modified by||PhysBrain (974)|