2014/05/07 by Ivan Kyrchei, Kyrchei, Ivan
Mathematics · #15A15 #15B33 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:15A15 #msc:15B33
paper · pdf · doi:10.48550/arxiv.1405.1614
arxiv created 2014/05/07 · arxiv updated 2014/05/08
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.