A survey of some recent results on Clifford algebras in R^4

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F23%3A43928473" target="_blank" >RIV/60461373:22340/23:43928473 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.21136/AM.2023.0182-22" target="_blank" >https://link.springer.com/article/10.21136/AM.2023.0182-22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/AM.2023.0182-22" target="_blank" >10.21136/AM.2023.0182-22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A survey of some recent results on Clifford algebras in R^4

Popis výsledku v původním jazyce

We will study applications of numerical methods in Clifford algebras in, in particular in the skew field of quaternions, in the algebra of coquaternions and in the other nondivision algebras in. In order to gain insight into the multidimensional case, we first consider linear equations in quaternions and coquaternions. Then we will search for zeros of one-sided (simple) quaternion polynomials. Three different classes of zeros can be distinguished. In general, the quaternionic coefficients can be placed on both sides of the powers. Then there are even five different classes of zeros. All results can be extended to other noncommutative algebras in. In the paper by R. Lauterbach and G. Opfer (2014), the authors constructed an exact Jacobi matrix for functions defined in noncommutative algebraic systems without the use of any partial derivative. We applied this technique to find the eigenvalues of the companion matrix as zeros of the companion polynomial by Newton’s method.

Název v anglickém jazyce

A survey of some recent results on Clifford algebras in R^4

Popis výsledku anglicky

We will study applications of numerical methods in Clifford algebras in, in particular in the skew field of quaternions, in the algebra of coquaternions and in the other nondivision algebras in. In order to gain insight into the multidimensional case, we first consider linear equations in quaternions and coquaternions. Then we will search for zeros of one-sided (simple) quaternion polynomials. Three different classes of zeros can be distinguished. In general, the quaternionic coefficients can be placed on both sides of the powers. Then there are even five different classes of zeros. All results can be extended to other noncommutative algebras in. In the paper by R. Lauterbach and G. Opfer (2014), the authors constructed an exact Jacobi matrix for functions defined in noncommutative algebraic systems without the use of any partial derivative. We applied this technique to find the eigenvalues of the companion matrix as zeros of the companion polynomial by Newton’s method.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

1572-9109

Svazek periodika

68

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

22

Strana od-do

571-592

Kód UT WoS článku

001049773800001

EID výsledku v databázi Scopus

2-s2.0-85168122218