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Algorithms for finding the roots of some quadratic octonion equations. (English) Zbl 1305.15042

This paper is focused on finding the solutions of the quadratic equations \(x^2+bx+c=0\) and \(xax+bx+c=0\) over the non-commutative and non-associative 8-dimensional algebra of octonions. Necessary and sufficient conditions for the existence of one, two or infinitely many solutions are given. However, the main contribution is to provide MATLAB oriented algorithms for computing the solutions of those octonionic equations and also for computing the product of octonions.

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
65H04 Numerical computation of roots of polynomial equations

Software:

Matlab
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Full Text: DOI

References:

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