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

关键词:  亏损矩阵  幂级数  若当链  固定矩阵

Key words:  defective matrix  power series  Jordan chain  regular matrix

摘要:

通过方阵A的极小多项式h(λ)=(λ-λ₁)^n₁(λ-λ₂)^n₂…(λ-λ_s)^n_s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A^m=PJ^mP^-1改进为A^m=V(m)D^-1(E,A,…,A^w-1)^T,免去求若当链及P^-1的步骤.

Abstract:

Define the transformable entries vector V(m) on the basis of index of the minimal polynomial h(λ)=(λ-λ₁) ^n₁ (λ -λ₂) ^n₂ … (λ -λ_s) ^n_s,and make up the regular matrix D The classics formula A^m=PJ^m P^-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.