Research Information System
Mathematical Sciences Letters, vol.3, no.3, pp.147-156, 2014 (Peer-Reviewed Journal)
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 equations 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.