实数域上亏损矩阵幂的一个简洁表示

A Concise Expression for Power of Defective Matrix in Real Number Field

研究实数域上亏损矩阵的幂的算法。考虑到不易从它的特征多项式获得构成广义若当标准型的阶数更小的广义若当块的有关信息,针对矩阵乘法不满足交换率,本文从计算广义若当标准型的幂的一般形式出发,获得实数域上亏损矩阵的幂的一个简洁表示。

In this paper, the power of a defective matrix in real number field is studied. Since the information for the generalized Jordan canonical blocks in the generalized Jordan canonical form can not be easily obtained from the characteristic polynomial and the commutative law does not hold for matrix multiplication, we compute the common form of the power of the generalized Jordan canonical form and get a concise expression for the power of the defective matrix.