Decomposition of Singular Matrices into Idempotents
نویسندگان
چکیده
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 ([12]) and Rao ([3]) to noncommutative setting and fill in the gaps in the original proof of Rao’s main theorems (cf. [3], Theorems 5 and 7 and [4]). We also consider singular matrices over Bézout domains as to when such a matrix is a product of idempotent matrices.
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