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

2013/07/16 by Ivan Kyrchei, Kyrchei, Ivan
Computer Science · Mathematics · #15A15 #16W10 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1307.4281

openalex publication_date 2013/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quaternions and matrices of quaternions

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