P-canonical forms and Drazin inverses

2020/07/20 by Mohammed Mouçouf, Moucouf, Mohammed · 1 citation
Computer Science · Mathematics · #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.2007.10199

openalex publication_date 2020/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, P-canonical forms of (A^k)_k (or simply of the matrix A) are defined and some of their properties are proved. It is also shown how we can deduce from them many interesting informations about the matrix A. In addition, it is proved that the P-canonical forms of A can be written as a sum of two parts, the geometric and the non-geometric parts of A, and that the P-canonical form of the Drazin inverse A_d of A can be deduced by simply plugging -k for k in the geometric part of A. Finally, several examples are provided to illustrate the obtained results.

Citations

• Pseudo-Inverses in Associative Rings and Semigroups

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