Products of nilpotent matrices

Robert Sullivan

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)311-317
    JournalLINEAR & MULTILINEAR ALGEBRA
    Volume56
    Issue number3
    DOIs
    Publication statusPublished - 2008

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