Upper Bounds on Eigenvalue Variation

摘要：

Let A and A~= D1*AD2 be two nx n diagonal-izable matrices with eigendecomposition A = XAA-1 and A = XAX~1, where D1, D2, X and X are nonsingular, and A = diag(λ1,...,λn) and A = diag(λ1,... ,λn). Li 1 proved that if λ1 > λ2 > ...≥ λn≥0 and λ1 > λ2 > ... ≥ λn ≥ 0, then max1≥j≥n|λj-λj/λj|≤||X-1||2||X||2||D2||2 x||X-1(D1*-D2-1)X||2, In this note, we show that the bounds are valid under slightly more general conditions.

关键词： diagonalizable matrices eigenvalues spectral norm

作者: Guoxing Wu Yinyin Huang Duanmei Zhou Yanjun Yan

作者单位: Department of Mathematics Northeast Forestry University, 150040,Harbin, China

会议类型: 国际会议

会议名称: The Fourth International Joint Conference on Computational Science and Optimization(第四届计算科学与优化国际大会 CSO 2011)

会议地点: 昆明、丽江

会议语种:英文

页码: 34-36

在线出版日期: 2011-04-15（万方平台首次上网日期，不代表论文的发表时间）