A Note on the Solutions of Some Linear Octonionic Equations

Abstract

The main concerns of this paper are the linear equations with one term and one unknown of the forms: α(xα) = ρ, α(xβ) = ρ and (αx) β = ρ, and the linear equations with two terms and one unknown of the forms: (αx) β +(γx) δ = ρ and α (xβ)+ γ(xδ) = ρ over the octonion field. Explicit general solutions of the eq uations in forms α(xα) = ρ, α(xβ) = ρ and (αx) β = ρ are given, and solutions of the octonionic equations form (αx) β +(γx) δ = ρ and α(xβ)+ γ(xδ) = ρ by matrix representation of octonions are derived using some particular cases. Examples of numerical equations are considered.