jafari, mehdi afagh higher education institute - department of mathematics, ايران

On The Structure Of The Octonion Matrices

28344

Octonions have applications in fields such as string theory, special relativity, and quantum logic. With the aid of the Hamilton operators, real octonions have been expressed in terms of 8×8 matrices. These matrices are being used to describe the rotation and determine a homothetic motions in 8- dimensional Euclidean space E8. In this paper, we study some algebraic properties of real octonions, and by using De Moivre s formula, we obtain any power of such matrices. Also, a relation between the powers of matrices of octonions is given. The De Moivre s formula implies that there are uncountably many matrices of the unit octonions A satisfying A^n = I8 for every integer n ≥ 3.

51

De , Moiver’s formula , Euler’s formula , Real octonion , Hamilton Operator

Erciyes University Journal Of The Institute Of Science an‎d Technology

63