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Nilpotent factorization of matrices. (English) Zbl 0754.15009

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.

MSC:

15A23 Factorization of matrices

Citations:

Zbl 0628.15008
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References:

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[8] DOI: 10.1016/0024-3795(87)90346-6 · Zbl 0628.15008 · doi:10.1016/0024-3795(87)90346-6
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