A Note on the Solutions of Some Linear Octonionic Equations

Bolat C., İpek A.

Mathematical Sciences Letters, cilt.3, sa.3, ss.147-156, 2014 (Hakemli Dergi)

Özet

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.