For every $p(x)\in F[x]$ where $F$ is a field , can we always find a integer $n$ and a matrix $A\in M_n(F)$ such that $p(A)=0$?
2026-04-09 05:26:14.1775712374
For every polynomial $p$ find a matrix $A$ such that $p(A)=0$
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Yes : Take the companion matrix of the coefficients of $p$.