Matrix representation of octonions and generalizations

Jamil Daboul, Robert Delbourgo

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We define a special matrix multiplication among a special subset of 2N×2N matrices, and study the resulting (nonassociative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative nonassociative, and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers; they naturally lead to the Cayley-Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac's equation for a free particle. A few other results and remarks arise as byproducts.

Original languageEnglish
Pages (from-to)4134-4150
Number of pages17
JournalJournal of Mathematical Physics
Issue number8
StatePublished - 1 Jan 1999

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Matrix representation of octonions and generalizations'. Together they form a unique fingerprint.

Cite this