利用固定矩阵计算亏损矩阵的幂级数之和

The Sum Of the Defective Matrix Power Series by the Regular Matrix

通过方阵 A的极小多项式φ(λ) =(λ-λ1 ) n1 (λ -λ2 ) n2 … (λ -λs) ns的指数来定义可变系数向量 V(m) ,并构成 A的固定矩阵 D.利用固定矩阵 D,将计算亏损矩阵的幂级数公式 Am=PJm P- 1 改进为 Am=V(m) D- 1 (E,A,… ,Aw- 1 ) T,免去求若当链及 P- 1的步骤 .

Define the transformable entries vector V(m) on the basis of index of the minimal polynomial φ(λ)=(λ-λ\-1) n\-1 (λ-λ\-2) n\-2 …(λ-λ\-s) n\-s ,and make up the regular matrix D The classics formula A\+m=PJ\+mP -1 is improved to A\+m=V(m)D -1 (E,A,…,A w-1 \+T Accordingly,the calculation of the Jordan chains and P -1 can be avoided.