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A Note on the Solutions of Some Linear Octonionic Equations |
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PP: 147-156 |
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Author(s) |
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Cennet Bolat,
Ahmet İPEK,
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Abstract |
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| 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. |
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