Matrix/Field/Characteristic polynomial/Definition

For an ${\displaystyle {}n\times n}$-matrix ${\displaystyle {}M}$ with entries in a field ${\displaystyle {}K}$, the polynomial

${\displaystyle {}\chi _{M}:=\det {\left(X\cdot E_{n}-M\right)}\,}$

is called the characteristic polynomial of ${\displaystyle {}M}$.