利用线性方程组计算极小多项式

A Way For Minimal Polynomial By Linear Equations

设n阶方阵A的特征多项式为∏si=1(λ-λi)ci,λi对应的幂零阵Ahi(h=0,1,…,ci-1)可通过解固定的n阶线性方程组求得.若Anii=O而Ani-1i≠O,则A的极小多项式为∏si=1(λ-λi)ni.

Assumed the characteristic polynomial of n order matrix A be ∏si=1(λ-λ_i)^(c_i). The nilpotent matrixes A^h_i(h=0,1,…,c_i-1) of λ_i are got by the solution of regular n order system linear equations. If A^(n_i)_i=O but A^(n_i-1)_i≠O, the minimal polynomial of A is ∏si=1(λ-λ_i)^(n_i).