NDLI: Construction of Octonionic Polynomials

Content Provider	Springer Nature Link
Author	Serôdio, Rogério
Copyright Year	2008
Abstract	In a previous paper “[On Octonionic Polynomials”, Advances in Applied Clifford Algebras, 17 (2), (2007), 245–258] we discussed generalizations of results on quaternionic polynomials to the octonionic polynomials. In this paper, we continue this generalization searching for methods to construct octonionic polynomials with a prescribed set of zeros.Two iterative methods, valid for the quaternions, are applied to construct octonionic polynomials with limited results. The non-associativity of the octonion product does not allow the prescribed set of zeros to be the set of zeros of the constructed polynomial. Nevertheless, we will show that one of the methods has some advantage relatively to the other.Finally, a closed form method is given to construct an octonionic polynomial with a prescribed set of zeros. This method requires the inversion of a block Vandermonde matrix. The necessary and sufficient conditions for the existence of the inverse are studied.
Ending Page	178
Page Count	24
Starting Page	155
File Format	PDF
ISSN	01887009
e-ISSN	16614909
Journal	Advances in Applied Clifford Algebras
Issue Number	1
Volume Number	20
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2008-11-05
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	zeros of polynomials Mathematical Methods in Physics block Vandermonde matrix polynomials octonions Theoretical, Mathematical and Computational Physics Linear algebraic groups over the reals, the complexes, the quaternions Applications of Mathematics Quaternion and other division algebras: arithmetic, zeta functions Division algebra Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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