On the Lengths of Pairs of Complex Matrices of Size at most Five

William Longstaff, Alice Niemeyer, Oreste Panaia

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    The length of every pair {A, B} of n×n complex matrices is at most 2n − 2, if n ≤ 5. That is, for n ≤ 5, the (possibly empty) words in A, B of length at most 2n − 2 span the unital algebra  generated by A, B. For every positive integer m there exist m×m complex matrices C, D such that the length of the pair {C, D} is 2m – 2.
    Original languageEnglish
    Pages (from-to)461-472
    JournalBulletin of the Australian Mathematical Society
    Volume73
    DOIs
    Publication statusPublished - 2006

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