Advanced Linear Algebra
《Advanced Linear Algebra》 · 第 165-166 页 · Chapter 7「Orders and the Minimal Polynomial」
In treatments of linear algebra that do not emphasize the role of the module $M_\tau$, the minimal polynomial of a linear operator $\tau$ is simply defined as the unique monic polynomial $m_\tau(x)$ of smallest degree for which $m_\tau(\tau)=0$. … The minimal polynomial $m_A(x)$ of matrix $A\in M_n(F)$ is defined as the minimal polynomial of the multiplication operator $\tau_A$. Equivalently, $m_A(x)$ is the unique monic polynomial $p(x)\in F[x]$ of smallest degree for which $p(A)=0$.