The maximum dimension of a subspace of nilpotent ...
|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|
|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.|
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