Sourour, A. R. Nilpotent factorization of matrices. (English) Zbl 0754.15009 Linear Multilinear Algebra 31, No. 1-4, 303-308 (1992). A square matrix \(N\) is called nilpotent if \(N^ m=0\) for some positive integer \(m\). A result due to P. Y. Wu [Linear Algebra Appl. 96, 227-232 (1987; Zbl 0628.15008)] is that, with the exception of \(2\times 2\) nilpotent matrices of rank one, every singular square matrix over the complex field is a product of two nilpotent matrices, which in addition may be taken to have the same rank as \(A\). In the present paper the authors shows that the same conclusion holds for matrices over an arbitrary field. Reviewer: J.A.Ball (Blacksburg) Cited in 2 ReviewsCited in 7 Documents MSC: 15A23 Factorization of matrices Keywords:nilpotent factorization; singular square matrix; product of two nilpotent matrices; matrices over an arbitrary field Citations:Zbl 0628.15008 PDFBibTeX XMLCite \textit{A. R. Sourour}, Linear Multilinear Algebra 31, No. 1--4, 303--308 (1992; Zbl 0754.15009) Full Text: DOI Link References: [1] Fong C. K., Proc. Ray. Soc. Edinburgh 99 pp 193– (1984) [2] Hoffman K., Linear Algebra (1971) [3] Laffey T. J., NATO ASI Series (1991) [4] DOI: 10.1090/S0002-9939-1969-0240116-9 · doi:10.1090/S0002-9939-1969-0240116-9 [5] Radjavi H., Proc. Amer. Math. Soc. 26 pp 701– (1970) [6] DOI: 10.1080/03081088608817711 · Zbl 0591.15008 · doi:10.1080/03081088608817711 [7] Sourour A. R., Proc. Amer. Math. Soc. 19 (1986) [8] DOI: 10.1016/0024-3795(87)90346-6 · Zbl 0628.15008 · doi:10.1016/0024-3795(87)90346-6 [9] DOI: 10.1016/0024-3795(89)90546-6 · Zbl 0673.47018 · doi:10.1016/0024-3795(89)90546-6 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.