A note on products of quadratic matrices of singular type

2019/02/10 by Hattingh, Christiaan J
#15-02 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1902.03584

Abstract

I provide an alternate and self-contained proof of Botha's theorem on products of idempotent and square-zero matrices where the product contains two square-zero factors, and provide a conclusive characterisation of products of singular quadratic matrices based on previous results.

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• Sums and products of square-zero matrices
• A note on Products of Nilpotent Matrices
• Decomposition of singular matrices into idempotents
• The sum and the product of two quadratic matrices
• Effectively bounded idempotent generation of certain 2 \× 2\n singular matrices by idempotent matrices over real quadratic number rings