An algorithm for solution of the Sylvester s$$ s $$-conjugate linear equation for the commutative elliptic octonions

Abstract

In this study, firstly, algebraic properties for commutative elliptic octonions are studied. Then the definition and theorems related to similarity, consimilarity, semisimilarity, and consemisimilarity are given. The matrix algebra for commutative elliptic octonions is established. The Sylvester 7-conjugate equation is solved in the commutative elliptic octonion space through an isomorphism established between the set of matrices and the set of commutative elliptic octonions. Additionally, an example is provided to support this solution. Finally, an algorithm is written for solving the Sylvester 7-conjugate equation.