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Figure 4
(a) Example of a 3D vector space with orthonormal basis vectors [{\hat \gamma}_1, {\hat \gamma}_2, {\hat \gamma}_3] which expands under the operation of geometric product (multiplication) of vectors to a 2n = 8D algebraic vector space, (b), that is closed under geometric product. Objects in this space are called multivectors (or Clifford numbers), whose algebra is called Clifford algebra (CA). A blade is a scalar, a vector or the wedge product of any number of vectors. The grade of a blade refers to the number of vectors composing the blade. (c) The number of blades of different grades forming the basis for a 2n-dimensional CA is given by the Pascal's triangle. The correct sequential notation for blades in increasing order of grade is scalar (S), vector (V), bivector (B), trivector (T), quadvector (Q) … blade of grade n (N). A general multivector in CA is a blade or a sum of blades.

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ISSN: 2053-2733
Volume 76| Part 3| May 2020| Pages 318-327
https://doi.org/10.1107/S205327332000217X
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