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The 8 $\times$ 8 matrix representation of SO(8) Symmetry has been defined byusing the direct product of Pauli matrices and Gamma matrices. These 8 $\times$8 matrices are being used to describe the rotations in SO(8) symmetry. Thecomparison of 8$\times$8 matrices with octonions has also been shown. Thetransformations of SO(8) symmetry are represented with the help of Octonionsand split Octonions spinors.

Octonion and Split Octonion Representation of SO(8) Symmetry