摘要
非亏损矩阵A可分解成特征矩阵之和 ,根据范德蒙矩阵与Am=λ1m -1A1+λ2 m -1A2 +… +λsm -1As 得出计算矩阵方幂的公式Am=((λ1m -1,λ2 m -1,…λsm -1)D-1) E) (A ,A2 …As) T。本文给出用特征矩阵分解与初等行变换求A的一系列幂的简捷方法。
The non-defective matrix can be decomposed into the sum of the characteristic matrixes. The operational formula for its power A m=(((λ m-1 1,λ m-1 2,…,λ m-1 s)D -1 )E)(A,A 2,…,A s) T is proved on the basic of Vandermonde matrix and A m=λ m-1 1A 1+λ m-1 2A 2+…+λ m-1 sA s. This paper shows some simple methods to calculate the powers of A using the characteristic matrix decomposition and the elementary row operation.
出处
《河池师专学报》
2003年第4期72-74,78,共4页
Journal of Hechi Normal College
关键词
特征根
非亏损矩阵
特征矩阵
幂
分解
characrteristic value
non-defective matrix
characteristic matrix
power
