在线性代数中，对一个线性自同态（取定基即等价于方阵）可定义其特征多项式，此多项式包含该自同态的一些重要性质，例如行列式、迹数及特征值。

设 为域（例如实数或复数域），对布于 上的 矩阵 ，定义其特征多项式为

这是一个 次多项式，其首项系数为一。

一般而言，对布于任何交换环上的方阵都能定义特征多项式。

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix as coefficients. The characteristic polynomial of an endomorphism of vector spaces of finite dimension is the characteristic polynomial of the matrix of the endomorphism over any base; it does not depend on the choice of a basis. The characteristic equation is the equation obtained by equating to zero the characteristic polynomial.