Abstract
In this paper a wide class of matrices is considered, containing idempotent, involutory, nilpotent and several other types of matrices. Extending an approach considered by Radjavi and Rosenthal [H. Radjavi, P. Rosenthal, On commutators of idempotents, Linear Multilinear Algebra 50 (2) (2002) 121–124], we investigate the set Q ( P ) of square matrices A ∈ C n × n satisfying the equation A 2 = α A + β P for some complex numbers α and β and for some n × n nonzero complex idempotent matrix P such the AP = PA = A . Special attention is paid to the Moore–Penrose and group inverse of matrices belonging to Q ( P ) .
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