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\begin{document}

\title{Algorithm of Order 3 Matrix in a Chosen Basis}



\author[1]{Ruslan Pozinkevych}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 15, 2024}


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\begin{abstract}
The aim of our research is to establish relationship between linearly
independent vectors and the~R\textsuperscript{3} Space The means for
that are going to be taken from Balanced Ternary analysis e.g. triplets
with entries (-1,0,1) This is not going to be any specific vector, for
instance (-1,0,1) It's going to be rather a Coordinate system with 8
quadrants and directional vectors The novelty of the proposed research
lies in the fact that unlike traditional Cartesian system-vector basis
our system uses 8 vectors which are at the same time a polyvector (Boas)
We may define it as a multiple of the type:~ [?] (i=-1)\^{}1[?] (j=-1)\^{}1
[?] (k=-1)\^{}1\begin{CJK}{UTF8}{gbsn}〖\end{CJK}\selectlanguage{english}(i,j,k)\begin{CJK}{UTF8}{gbsn}〗 \end{CJK}\selectlanguage{english}~%
\end{abstract}%



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\textbf{Hosted file}

\verb`Algorithm of Order 3 Matrix in a Chosen Basis Cr1.docx`  available at \url{https://authorea.com/users/770917/articles/848737-algorithm-of-order-3-matrix-in-a-chosen-basis}

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