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arXiv · 1307.4281

Determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field with applications

Ivan Kyrchei
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Abstract

Within the framework of the theory of the column and row determinants, we obtain determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field. Using the obtained determinantal representations of the Drazin inverse we get explicit representation formulas (analogs of Cramer's rule) for the Drazin inverse solutions of quaternion matrix equations $ {\bf A}{\bf X} = {\bf D}$, $ {\bf X}{\bf B} = {\bf D} $ and ${\bf A} {\bf X} {\bf B} = {\bf D} $, where $ {\bf A}$, ${\bf B}$ are Hermitian.

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Ivan Kyrchei. 2013-07-16. Determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field with applications. https://arxiv.org/abs/1307.4281

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