The maximum dimension of a subspace of nilpotent ...

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Title The maximum dimension of a subspace of nilpotent matrices of index 2
Author(s) L. G. Sweet, J. A. MacDougall
Journal Linear Algebra and its Applications
Date 2009
Volume 431
Issue 8
Start page 1116
End page 1124
Abstract A matrix M is nilpotent of index 2 if M2=0. Let V be a space of nilpotent n×n matrices of index 2 over a field k where 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 . 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.
DOI 10.1016/j.laa.2009.03.048

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