<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Bounds for the zeros of unilateral octonionic polynomials

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Bounds for the zeros of unilateral octonionic polynomials"}

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...

Bounds for the zeros of unilateral octonionic polynomials

Published Online: Nov 23, 2021

Page range: 243 - 267

Received: Apr 06, 2021

Accepted: Apr 30, 2021

DOI: https://doi.org/10.2478/auom-2021-0043

Keywords
Octonions, octonionic polynomials, matricial norms, bounds for the zeros

© 2021 Rogério Serôdio et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Bounds for the zeros of unilateral octonionic polynomials

Published Online: Nov 23, 2021

Page range: 243 - 267

Received: Apr 06, 2021

Accepted: Apr 30, 2021

DOI: https://doi.org/10.2478/auom-2021-0043

KeywordsOctonions, octonionic polynomials, matricial norms, bounds for the zeros

© 2021 Rogério Serôdio et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Octonions, octonionic polynomials, matricial norms, bounds for the zeros