Inifnite hypercomplex number system factorization methods
Yakiv O. Kalinovsky, Dmitry V. Lande, Yuliya E. Boyarinova, Iana V., Khitsko
TL;DR
This paper presents a method for factorizing infinite hypercomplex number systems into finite systems, enabling reduction in dimensionality and generating noncanonical systems starting from the third dimension.
Contribution
It introduces a novel approach to convert infinite hypercomplex systems into finite ones and re-factorize even-dimensional systems to reduce their dimension.
Findings
Noncanonical hypercomplex systems are obtained from the third dimension onward.
Even-dimensional hypercomplex systems can be re-factorized to lower their dimension.
The method enables systematic generation and reduction of hypercomplex systems.
Abstract
The method of obtaining the set of noncanonical hypercomplex number systems by conversion of infinite hypercomplex number system to finite hypercomplex number system depending on multiplication rules and factorization method is described. Systems obtained by this method starting from the 3rddimension are noncanonical. The obtained systems of even dimension can be re-factorized. As a result of it hypercomplex number system of two times less dimension are got.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Numerical Methods and Algorithms · Mathematical and Theoretical Analysis