MONOMIAL (1, 0,-1) MATRIX OF THE FOURTH ORDER, ISOMORPHIC TO THE GROUP OF QUATERNIONS

Authors

  • V. V. Kravets Ukrainian State University of Chemical Technology, Dnipropetrovsk
  • T. V. Kravets Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan
  • O. V. Kharchenko Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan

DOI:

https://doi.org/10.15802/stp2009/13638

Keywords:

monomial matrix, matrix of the fourth order, isomorphic to the group, quaternion

Abstract

A set of direct and inverse elements are examined and compared with a four-dimensional orthonormal basis. The aggregate of even substitutions of fourth power as a product of two transpositions are formed on this finite set. The finite set of substitutions is represented by monomial (1, 0, –1)-matrices of fourth order. An isomorphism of quaternion group and two noncommutative subgroups of eighth order is determined. Properties of four aggregates of basic matrices, corresponding to quaternion matrices, are examined.

Author Biographies

V. V. Kravets, Ukrainian State University of Chemical Technology, Dnipropetrovsk

V. V. Kravets

T. V. Kravets, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan

T. V. Kravets

O. V. Kharchenko, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan

O. V. Kharchenko

Published

2009-10-25

How to Cite

Kravets, V. V., Kravets, T. V., & Kharchenko, O. V. (2009). MONOMIAL (1, 0,-1) MATRIX OF THE FOURTH ORDER, ISOMORPHIC TO THE GROUP OF QUATERNIONS. Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport, (29), 154–158. https://doi.org/10.15802/stp2009/13638

Issue

Section

TRANSPORT AND ECONOMIC TASKS MODELING