ROW DETERMINANT OF THE MATRIX OF THE N-TH ORDER OF MATRICES DEFINED OVER THE BODY OF QUATERNION NUMBERS AND ITS PROPERTIES: ROW DETERMINANT OF THE MATRIX OF THE N-TH ORDER OF MATRICES DEFINED OVER THE BODY OF QUATERNION  ....

doi:10.56292/SJFSU/vol31_iss4/a%p

Authors

Saidakhbor Juraboev

Fergana State University

https://orcid.org/0000-0002-2445-749X
Farg'ona davlat universiteti

https://orcid.org/0009-0007-6002-3246
Mrs.

Farg'ona davlat universiteti

https://orcid.org/0009-0006-3383-2454

DOI:

https://doi.org/10.56292/SJFSU/vol31_iss4/a%25p

Keywords:

quaternion number; quaternion matrix; row determinant

Abstract

This paper studies the row determinant of square matrices defined over the skew field of quaternion numbers and its properties. The row determinant of a square matrix by the -row is defined as the algebraic sum of products of elements taken from each row of the square matrix, once. Each row determinant by the -row has different values and differs from the determinant of a commutative matrix. At the same time, some properties are preserved. These properties were proved using the definition of row determinants

Author Biographies

Saidakhbor Juraboev, Fergana State University

Farg‘ona davlat universiteti, fizika-matematika fanlari bo ‘yicha falsafa doktori, (PhD)
, Farg'ona davlat universiteti

Farg‘ona davlat universiteti talabasi
Mrs., Farg'ona davlat universiteti

Farg‘ona davlat universiteti 3-bosqich talabasi

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ROW DETERMINANT OF THE MATRIX OF THE N-TH ORDER OF MATRICES DEFINED OVER THE BODY OF QUATERNION NUMBERS AND ITS PROPERTIES