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Polynomial equations over octonion algebras.
- Source :
-
Journal of Algebra & Its Applications . Jun2020, Vol. 19 Issue 6, pN.PAG-N.PAG. 10p. - Publication Year :
- 2020
-
Abstract
- In this paper, we present a complete method for finding the roots of all polynomials of the form ϕ (z) = c n z n + c n − 1 z n − 1 + ⋯ + c 1 z + c 0 over a given octonion division algebra. When ϕ (z) is monic, we also consider the companion matrix and its left and right eigenvalues and study their relations to the roots of ϕ (z) , showing that the right eigenvalues form the conjugacy classes of the roots of ϕ (z) and the left eigenvalues form a larger set than the roots of ϕ (z). [ABSTRACT FROM AUTHOR]
- Subjects :
- *POLYNOMIALS
*CAYLEY numbers (Algebra)
*ALGEBRA
*EQUATIONS
*CONJUGACY classes
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 19
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 144403936
- Full Text :
- https://doi.org/10.1142/S0219498820501029