A survey of some recent results on Clifford algebras in R^4
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
A survey of some recent results on Clifford algebras in R^4
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
1572-9109
Volume of the periodical
68
Issue of the periodical within the volume
August
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
22
Pages from-to
571-592
UT code for WoS article
001049773800001
EID of the result in the Scopus database
2-s2.0-85168122218