2024/03/21 by D. E. Ferreyra, Dijana Mosić, Ferreyra, D. E. +1
Computer Science · Mathematics · #15A09 #15A10 #15A24 #15A30 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2403.14196
openalex publication_date 2024/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Malik and Ferreyra introduced the m-weak core inverse for complex square matrices which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. The main aim of this paper is to extend the concept of m-weak core inverse for complex rectangular matrices. This extension is called the W-weighted m-weak core inverse. We analyse its existence and uniqueness as solution of a system of matrix equations. We present various properties, representations and characterizations of the W-weighted m-weak core inverse, as well as its applications in solving certain matrix systems. A canonical form of the W-weighted m-weak core inverse is also provided by using a simultaneous unitary block upper triangularization of a pair of rectangular matrices.