基于矩阵幂运算的重特征值存在性定理

对于判断矩阵重特征值的存在性问题，运用“若λ是矩阵A的特征值，则入“是Ak的特征值”这一性质，通过矩阵的迹与特征值的关系，得到了实数域上矩阵重特征值的存在性定理并给出了证明．定理实现了“由矩阵幂运算来判断矩阵重特征值的存在性”这样一个计算过程，对讨论矩阵特征值问题具有一定的启示意义．

Powers of matrices on the existence of multiple eigenvalues

In order to judge the existence problem of matrix eigenvalues,we using the nature of ＂if λ is the eigenvalues of matrix A, then λk is the eigenvalues of Ak＇＇, by means of the relationship between the trace and the eigenvalues matrix, we obtain the existence theorems of real number field matrix eigenvalues, and the proof is given. The theorem of the realization of such a calculation process ＂By the matrix exponentiation to judge the existence of matrix repeated eigenvalues＂, has certain enlightenment significance to the repeated eigenvalues matrix.