具有相同特征值的矩阵的刻画

摘要

文章首先给出关于多项式的牛顿恒等式新的证明,利用牛顿恒等式和矩阵的迹的性质,得出两个矩阵具有相同特征值的充分必要条件.%In this paper, a new simple proof of Newton＇s identities is given. Moreover, it also obtains a characterize of matrices with the same eigenvalues, based on the properties of the Newton＇s identities and traces of matrices.