On the dimension of linear spaces of nilpotent matrices

Title: On the dimension of linear spaces of nilpotent matrices
Creator: MacDonald, G. W.; MacDougall, J. A.; Sweet, L. G.
Relation: Linear Algebra and Its Applications Vol. 436, Issue 7, p. 2210-2230
Publisher Link: http://dx.doi.org/10.1016/j.laa.2011.10.028
Publisher: Elsevier
Resource Type: journal article
Date: 2012
Description: We obtain bounds on the dimension of a linear space S of nilpotent n×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 a result of Mathes, Omladič, 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.
Subject: matrix; subspace; nilpotent; maximal dimension; rank; nilindex
Identifier: http://hdl.handle.net/1959.13/1327682
Identifier: uon:25721
Identifier: ISSN:0024-3795
Language: eng
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