Counting Symmetric Nilpotent Matrices

Andries E. Brouwer, Rod Gow, John Sheekey

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.

Keywords


Nilpotent; symmetric; matrix; endomorphism; enumeration

Full Text: PDF