MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.45, no.7, pp.4069-4080, 2022 (Peer-Reviewed Journal)
Article / Article
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
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Clifford algebras, Clifford product, multivector, norm, outer product, SUPPORT VECTOR MACHINES, CLASSIFICATION
In this paper, the equation.ex.y. = 1, such that x, y. Rn, is proved using defined group homomorphism and Euler's formula, where x. y is the outer product between x and y. Firstly, this equation is verified for n = 2, 3, 4,5 using Clifford product. Then, it turns out that it is difficult to maintain the proof in this way since the outer product is anticommutative, the size increases, and the calculation becomes a lot of work. For this reason, a group of homomorphism from the group C.. n, 0 to the group Rn,0 is described and used Euler's formula. Eventually, it is proved for any n. Z+ (n = 2) by generalizing this equation.