Wang, Qing-Wen; Zhang, Xiang; Zhang, Yang Algorithms for finding the roots of some quadratic octonion equations. (English) Zbl 1305.15042 Commun. Algebra 42, No. 8, 3267-3282 (2014). 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. Reviewer: João R. Cardoso (Coimbra) Cited in 2 Documents MSC: 15A24 Matrix equations and identities 15B33 Matrices over special rings (quaternions, finite fields, etc.) 65H04 Numerical computation of roots of polynomial equations Keywords:octonionic quadratic equations; octonions; MATLAB oriented algorithms Software:Matlab PDFBibTeX XMLCite \textit{Q.-W. Wang} et al., Commun. Algebra 42, No. 8, 3267--3282 (2014; Zbl 1305.15042) Full Text: DOI References: [1] DOI: 10.1090/S0273-0979-01-00934-X · Zbl 1026.17001 [2] DOI: 10.1007/BF03043104 · Zbl 0927.15007 [3] DOI: 10.1016/S0010-4655(98)00126-X · Zbl 1002.65046 [4] Dray T., Algebras Groups Geom. 19 pp 163– (2002) [5] Dray , T. , Janesky , J. , Manogue , C. A. ( 2000 ). Some properties of 3 {\(\times\)} 3 octonionic Hermitian matrices with non-real eigenvalues. Oregon State University, p. 12 . · Zbl 0984.15007 [6] DOI: 10.1007/s00006-000-0003-1 · Zbl 0984.15007 [7] DOI: 10.1080/03081081003739204 · Zbl 1237.15016 [8] DOI: 10.1016/S0893-9659(02)80003-9 · Zbl 1011.15010 [9] DOI: 10.1016/S0024-3795(00)00246-9 · Zbl 0976.15014 [10] Huang Z. J., J. Guangzhou Radio and TV Univ. 7 pp 44– (2007) [11] DOI: 10.2307/1968117 · Zbl 0008.42103 [12] DOI: 10.1007/BF03042010 · Zbl 0974.15012 [13] DOI: 10.1007/s00025-010-0041-5 · Zbl 1201.17019 [14] DOI: 10.1016/0024-3795(95)00543-9 · Zbl 0873.15008 [15] DOI: 10.1016/j.laa.2006.08.004 · Zbl 1117.15017 [16] Zhang , X. , Wang , Q. W. MATLAB: Octonion package, 2011 . This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.