矩阵秩和特征值的估计

Estimation for the Rank and Eigenvalues of Matrices

首先得到了特征值模的平方和的一个上界,接着给出了矩阵秩的一个下界,并用数值算例验证了所得结果的有效性,最后给出了矩阵特征值实部和虚部的估计.

An upper bound for the sum of squares of the module of eigenvalues of matrices is obtained.Meanwhile,a lower bound for the rank is given and the effectiveness of our result is confirmed with a numerical example.Finally,an estimation for the real part and the imaginary part of the eigenvalues is given.