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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14273 |
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Table of Contents:
- Let $F$ be the finite field of order $q$ and $\M(n,r, F)$ be the set of $n\times n$ matrices of rank $r$ over the field $F$. For $α\in F$ and $A\in \M(n,F)$, let $$Z^α_{A,r}=\left\{X\in \M(n,r, F)\mid \tr(AX)=α\right \}.$$ In this article, we solve the problem of determining the cardinality of $Z_{A,r}^α$. We also solve the generalization of the problem to rectangular matrices.