### Abstract

In 1975, Paul Halmos asked: when can a square matrix be written as a product of nilpotent matrices? This was answered indirectly by Sourour in 1992: if n >= 3 then any n x n singular matrix can be written in this way. In this article, we determine the best possible index for the nilpotents in such a product, and compare our work on linear transformations of a vector space with analogous results for transformations of a set.

Original language | English |
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Pages (from-to) | 311-317 |

Journal | LINEAR & MULTILINEAR ALGEBRA |

Volume | 56 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 |

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## Cite this

Sullivan, R. (2008). Products of nilpotent matrices.

*LINEAR & MULTILINEAR ALGEBRA*,*56*(3), 311-317. https://doi.org/10.1080/03081080701269548