Bounds for the zeros of unilateral octonionic polynomials

Author:

Serôdio Rogério1,Beites P. D.1,Vitória José2

Affiliation:

1. CMA and Departamento de Matemática , Universidade da Beira Interior , Rua Marquês d’Ávila e Bolama, 6201-001 Covilhã , Portugal .

2. University of Coimbra , Department of Mathematics , Apartado 3008, EC Santa Cruz, 3001-501 Coimbra , Portugal .

Abstract

Abstract In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.

Publisher

Walter de Gruyter GmbH

Reference35 articles.

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3. [3] Beites, P.D., Nicolás, A.P.: An associative triple system of the second kind. Commun. Algebra 44(11), 5027–5043 (2016).10.1080/00927872.2016.1149185

4. [4] Boukas, A, Fellouris, A.: On octonion polynomial equations. Int. J. Math. Comput. Sci. 1(2), 59–73 (2016).

5. [5] Cauchy, A.L.: Sur la résolution des équations numériques et sur la théorie de l’élimination. Exercices de Mathématiques. Chez de Bure frères, Paris, 65–128 (1829).

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