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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/916439

Title: The maximum dimension of a subspace of nilpotent matrices of index 2
Author/Creator: Sweet, L. G.; MacDougall, James A.
Institution: The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
Description: A matrix M is nilpotent of index 2 if M² = 0. Let V be a space of nilpotent n x n matrices of index 2 over a field k where card k > n and suppose that r is the maximum rank of any matrix in V. The object of this paper is to give an elementary proof of the fact that dim V ≤ r(n − r). We show that the inequality is sharp and construct all such subspaces of maximum dimension. We use the result to find the maximum dimension of spaces of anti-commuting matrices and zero subalgebras of special Jordan Algebras.
Relation: Linear Algebra and Its Applications Vol. 431, Issue 8, p. 1116-1124
Publisher Link: http://dx.doi.org/10.1016/j.laa.2009.03.048
Date: 2009
Publisher: Elsevier
Keyword(s): nilpotent matrix; matrix ranks
Resource Type: journal article
Identifier: http://hdl.handle.net/1959.13/916439
Identifier: ISSN:0024-3795

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