DocServer

ON THE DIMENSION OF LINEAR SPACES OF NILPOTENT MATRICES

MacDougall, James A. and MacDonald, G. W. and Sweet, L. G. (2010) ON THE DIMENSION OF LINEAR SPACES OF NILPOTENT MATRICES. .

[img]
Preview
PDF - Accepted Version
Download (227Kb) | Preview

    Abstract

    We obtain bounds on the dimension of a linear space S of nilpotent $n \times n$ matrices over an arbitrary field. We consider the case where bounds $k$ and $r$ are known for the nilindex and rank respectively, and find the best possible dimensional bound on the subspace S in terms of the quantities $n$, $k$ and $r$. We also consider the case where information is known concerning the Jordan forms of matrices in $S$ and obtain new dimensional bounds in terms of this information. These bounds improve known bounds of Gerstenhaber. Along the way, we generalize and give a new proof of a result Mathes, Omladi�c, and Radjavi concerning traces on subspaces of nilpotent matrices. This is a key component in the proof of our result and may also be of independent interest.

    Item Type: Article
    Subjects: 00-xx General > 00Axx General and miscellaneous specific topics
    Faculty: UNSPECIFIED
    Depositing User: Stephanie
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 28 Sep 2012 12:05
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/793

    Actions (login required)

    View Item