任意矩阵特征值的秩1修正扰动界

Eigenvalue Variations for Rankone Update of Arbitrary Matrices

摘要: 设A是一个n阶的任意复矩阵且E是A的Hermite秩1扰动，即E=xx,其中x是n维的复列向量，x是x的共轭转置向量.则A+E为矩阵A的Hermite秩1修正矩阵.基于矩阵分析理论中Hermite矩阵特征值分布的性质，研究得到了矩阵A特征值的任意Hermite秩1修正扰动的上下界限，即给出了矩阵A+E特征值的上下界限： SymbollAp_i(Euclid Math OneHAp(A))+l_i(x)+_iEuclid Math OneRAp(SymbollAp_i(A+

Abstract: Assume that matrix A is an arbitrary complex matrix of order n and E is a Hermitian rankone matrix, i.e., E=xx, where x is a complex column vector of order n and x is the conjugate transpose vector of x. So, A+E is called Hermitian rankone update of