Some applications of basic operations in Clifford algebra

Subject Areas : Algebraic geometry

T.  Manzoor ¹ (Department of Mathematics, Maulana Azad National Urdu University, Hyderabad-500032, India)
A.  Akg\"{u}l ² (Department of Mathematics, Art and Science Faculty, Siirt University, Siirt-56100, Turkey)

Received: 2022-03-04 Accepted : 2022-06-29 Published : 2022-06-01

Keywords: Contraction, Bivector, CA (GA), dualization, multivector, $g$-numbers, versor,

Abstract :

Geometric algebra provides intuitive and easy description of geometric entities (encoded by blades) along with different operations and orthogonal transformations. Grassmann's Exterior and Hamilton's quaternions lead to the existence of Clifford (Geometric) algebra. Clifford or geometric product has its significant role in whole domain of Clifford algebra, while as contraction (anti outer product or analogous to dot product) is grade reduction operation. The other operations can be derived from the former one. The paper explores elucidation of Clifford algebra and Clifford product with some salient features and applications.

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