The maximum dimension of a subspace of nilpotent ...
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Citation
| Title | The maximum dimension of a subspace of nilpotent matrices of index 2 |
| Author(s) | L. Sweet, J. 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 |
| ISSN | 0024-3795 |
Using APA 6th Edition citation style.
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