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arXiv · 1405.1614

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

Ivan Kyrchei
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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.

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Ivan Kyrchei. 2014-05-07. The column and row immanants of matrices over a split quaternion algebra. https://arxiv.org/abs/1405.1614

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