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 multipleMathworldPlanetmath grades. To distinguish the various graded entities, the blades are often prefixed by their grade. For example a grade-k basis entity would be called a k-blade.

The number of linearly independentMathworldPlanetmath k-blades in a particular geometric algebra is dependent on the number of dimensionsPlanetmathPlanetmath of the manifold on which the algebra is defined. For an n-dimensional manifold, the number of k-blades is given by the binomial coefficientMathworldPlanetmath.


The total number of basis blades of all grades in a geometric algebra defined on an n-manifold is then:

Title blade
Canonical name Blade
Date of creation 2013-03-22 15:58:40
Last modified on 2013-03-22 15:58:40
Owner PhysBrain (974)
Last modified by PhysBrain (974)
Numerical id 5
Author PhysBrain (974)
Entry type Definition
Classification msc 15A03
Classification msc 15A75
Classification msc 15A66
Related topic Basis
Related topic UnitVector