Question about condition number $k$ of a matrix over a finite field

Question

If $\lambda_{max}$, and $\lambda_{min}$ denote the maximum and minimum values of the eigenvalues of a normal square matrix repectively- are there any explicit bounds to the eigenvalues of such a square matrix, given the matrix is over a finite field, ie all the values in the matrix are in $GF(p)$ ($GF$ is Galois Field), and p is prime. Is there anything we can say about the condition number $k$ for a normal matrix over $GF(p)$?