Correspondence between Row-Column Determinants and Quasideterminants of Matrices over Quaternion Algebra

TL;DR

This paper explores the relationship between row-column determinants and quasideterminants in quaternion matrices, applying the theory to solve linear systems over quaternions and establishing key correspondences.

Contribution

It introduces a novel correspondence between row-column determinants and quasideterminants specifically for quaternion matrices, advancing the theoretical framework.

Findings

Established the correspondence between row and column determinants and quasideterminants.

Applied the theory to solve systems of linear equations over quaternion algebra.

Enhanced understanding of quaternion matrix determinants and their computational applications.

Abstract

In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion algebra. We established correspondence between row and column determinants and quasideterminants of matrix over quaternion algebra.