- Title
- The maximum dimension of a subspace of nilpotent matrices of index 2
- Creator
- Sweet, L. G.; MacDougall, James A.
- 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
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2009
- 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.
- Subject
- nilpotent matrix; matrix ranks
- Identifier
- uon:7996
- Identifier
- http://hdl.handle.net/1959.13/916439
- Identifier
- ISSN:0024-3795
- Reviewed
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