The column and row immanants of matrices over a split quaternion algebra

TL;DR

This paper extends the concepts of column and row immanants to matrices over split quaternion algebras, establishing their properties and key theorems for Hermitian matrices.

Contribution

It introduces new definitions of immanants for matrices over split quaternion algebras and proves fundamental properties and theorems related to Hermitian matrices.

Findings

Defined column and row immanants for split quaternion matrices

Proved key theorem for Hermitian matrices over split quaternion algebra

Introduced an immanant concept for Hermitian matrices in this setting

Abstract

The theory of the column-row determinants has been considered for matrices over a non-split quaternion algebra. In this paper the concepts of column-row determinants are extending to a split quaternion algebra. New definitions of the column and row immanants (permanents) for matrices over a non-split quaternion algebra are introduced, and their basic properties are investigated. The key theorem about the column and row immanants of a Hermitian matrix over a split quaternion algebra is proved. Based on this theorem an immanant of a Hermitian matrix over a split quaternion algebra is introduced.