Matrix representations of octonions and their applications
By Yongge Tian. 2000
98 citations recorded by the source corpus.
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 representations of quaternions. In this paper we give a complete investigation to real matrix representations of octonions, and consider their various applications to octonions as well as matrices of octonions.
Subfields: Applied Mathematics, Geometry and Topology, Mechanical Engineering
View Paper: https://www.semanticscholar.org/paper/9ce3f32a9012f39e2bae8ea24e3f7b3e0773c337
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In Applied Mathematics
In Geometry and Topology
In Mechanical Engineering
Citations in the corpus
- The Fibonacci Octonions (2015, background): “O is non-commutative, non-associative but it is alternative p (pq) = pq, (qp) p = qp, (pq) p = p (qp) := pqp, [6, 7].”