Matrix representations of octonions and their applications

  title={Matrix representations of octonions and their applications},
  author={Yongge Tian},
  journal={Advances in Applied Clifford Algebras},
  • Yongge Tian
  • Published 2000
  • Mathematics
  • Advances in Applied Clifford Algebras
As is well-known, the real quaternion division algebra ℍ is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra can not be algebraically isomorphic to any matrix algebras over the real number field ℝ, because is a non-associative algebra over ℝ. However since is an extension of ℍ by the Cayley-Dickson process and is also finite-dimensional, some pseudo real matrix representations of octonions can still be introduced through real matrix… Expand
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