Counting Symmetric Nilpotent Matrices

Andries E. Brouwer, Rod Gow, John Sheekey


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.


Nilpotent; symmetric; matrix; endomorphism; enumeration

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