De Moivre's and Euler's Formulas for the Matrices of Octonions

Abstract

The purpose of this paper is to obtain De Moivre's and Euler's formulas for the matrices of octonions, and to find the powers and the roots of these matrices. A simple method is provided to find the powers of 8x8 matrices with the help of De Moivre's formula obtained from the matrices of octonions. We also show that any powers of these matrices can be found. Furthermore, we get the square, cubic and n-th roots for the matrices of octonions.