Decomposition of singular matrices into idempotents

2013/01/23 by Adel Alahmadi, S.K. Jain, André Leroy · 3 citations
Mathematics · Computer Science · #Rings, Modules, and Algebras #Algebraic and Geometric Analysis #Matrix Theory and Algorithms

paper · doi:10.1080/03081087.2012.754439

Abstract

In this paper, we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey (Products of idempotent matrices. Linear Multilinear A. 1983) and Rao (Products of idempotent matrices. Linear Algebra Appl. 2009) to noncommutative setting and fill in the gaps in the original proof of Rao’s main theorems. We also consider singular matrices over Bézout domains as to when such a matrix is a product of idempotent matrices.

Cited by

• Idempotents in triangular matrix rings
• Strongly nil-clean 2-by-2 matrices over general commutative rings
• Products of idempotents in a quaternion ring

Related

• A Note on Idempotent Matrices: The Poset Structure and The Construction
• Idempotent factorization on some matrices over quadratic integer rings
• Decomposition of matrices into product of idempotents and separativity of regular rings
• Effectively bounded idempotent generation of certain 2 × 2 singular matrices by idempotent matrices over real quadratic number rings
• Triangular idempotent matrices over a general ring