Explicit formulas for determinantal representations of the Drazin\n inverse solutions of some matrix and differential matrix equations

2013/01/28 by Ivan Kyrchei, Kyrchei, Ivan
Chemistry · Computer Science · Mathematics · #15A15 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Molecular spectroscopy and chirality #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1301.6605

openalex publication_date 2013/01/28 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

The Drazin inverse solutions of the matrix equations rm bf A rm bf\nX = rm bf B, rm bf X rm bf A = rm bf B and rm\n bf A rm bf X rm bf B = rm bf D are considered in this\npaper. We use both the determinantal representations of the Drazin inverse\nobtained earlier by the author and in the paper. We get analogs of the Cramer\nrule for the Drazin inverse solutions of these matrix equations and using their\nfor determinantal representations of solutions of some differential matrix\nequations, bf X'+ bf A bf X= bf B and bf X'+ bf X bf A= bf\nB, where the matrix bf A is singular.\n

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