Determinantal representations of W-weighted Drazin inverse solutions of some quaternion matrix equations

2015/09/25 by Ivan Kyrchei, Kyrchei, Ivan
Computer Science · Materials Science · Mathematics · #15A15 #16W10 #Algebraic and Geometric Analysis #FOS: Mathematics #Liquid Crystal Research Advancements #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #math.RA #msc:15A15 #msc:16W10

paper · pdf · doi:10.48550/arxiv.1509.07883

arXiv admin note: substantial text overlap with arXiv:1503.03668

openalex publication_date 2015/09/25 · arxiv created 2016/02/22 · arxiv updated 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using determinantal representations of the W-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the W-weighted Drazin inverse solutions (analogs of Cramer's rule) of the quaternion matrix equations \bf W\bf A\bf W\bf X=\bf D, \bf X\bf W\bf A\bf W=\bf D , and \bf W₁\bf A\bf W₁\bf X\bf W₂\bf B\bf W₂=\bf D .

Citations

• A Drazin inverse for rectangular matrices
• New determinantal representations of the W-weighted Drazin inverse over the quaternion skew field

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