Hello, all!


I consider Hadamard product $A \circ B$ of matrices $A$, $B$ over finite field. I know $\det{A}$ and $\det{B}$ and want to know about $\det{(A \circ B)}$. Wikipedia and Google let me know properties about determinant for Hadamard product of positive-semidefinite matrices: $det{(A \circ B)} \ge \det{A} \cdot \det{B}$. What happens if matrices are over finite field?


Thank you.



Hadamard product of matrices over finite field
Given any $a$ and $b$, let $A=\pmatrix{a&0\cr0&1}$, $B=\pmatrix{0&-b\cr1&0}$, then $\det A=a$, $\det B=b$, and the determinant of the Hadamard product is zero. 


