Counting Symmetric Nilpotent Matrices Andries E. Brouwer Rod Gow John Sheekey DOI: https://doi.org/10.37236/3810 Keywords: Nilpotent, symmetric, matrix, endomorphism, enumeration Abstract We determine the number of nilpotent matrices of order $n$ over $\mathbb{F}_q$ that are self-adjoint for a given nondegenerate symmetric bilinear form, and in particular find the number of symmetric nilpotent matrices. PDF Published 2014-04-01 Issue Volume 21, Issue 2 (2014) Article Number P2.4