Elementary Transformation and its Applications for Hybrid number matrices

Abstract

In this paper, the elementary transformations of hybrid number matrix are defined and its upper triangularization process using the elementary transformation is given. Then, a new determinant is defined by means of a real representation matrix and the sufficient conditions for the existence of LU decompositions are summarized, followed by a counterexample that shows that hybrid number matrices do not have LU decomposition. Additionally, the inverse of the hybrid number matrix is studied and its existence condition and computation method are given.