DocumentCode :
2343292
Title :
Upper Bounds on Eigenvalue Variation
Author :
Wu, Guoxing ; Huang, Yinyin ; Zhou, Duanmei ; Yan, Yanjun
Author_Institution :
Dept. of Math., Northeast Forestry Univ., Harbin, China
fYear :
2011
fDate :
15-19 April 2011
Firstpage :
34
Lastpage :
36
Abstract :
Let A and à = D1*AD2 be two n × n diagonalizable matrices with eigendecomposition A = XΛX-1 and A = X̃Λ̃X̃-1, where D1, D2, X and X̃ are nonsingular, and Λ = diag(λ1,⋯, λn) and Λ̃ = diag(λ̃1L ⋯, λ̃n). Li [1] proved that if λ1 ≥ λ2 ≥ ⋯ ≥ λn ≥ 0 and λ1 ≥ λ2 ≥ ⋯ ≥ λn ≥ 0, then max1 ≤ j ≤ nj-λ̃jj| ≤ ∥X-12∥X̃∥2∥D22 × ∥X̃-1 (D1*-D2-1)X∥2, max1≤ j ≤ nj-λ̃j/λ̃j| ≤ ∥X-12∥X̃∥2∥D1-*2 × ∥X̃-1(D1*-D2-1)X∥2. In this note, we show that the bounds are valid under slightly more general conditions.
Keywords :
eigenvalues and eigenfunctions; matrix algebra; diagonalizable matrices; eigenvalue variation; upper bounds; Eigenvalues and eigenfunctions; Forestry; Joints; Linear algebra; Optimization; Upper bound; diagonalizable matrices; eigenvalues; spectral norm;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Computational Sciences and Optimization (CSO), 2011 Fourth International Joint Conference on
Conference_Location :
Yunnan
Print_ISBN :
978-1-4244-9712-6
Electronic_ISBN :
978-0-7695-4335-2
Type :
conf
DOI :
10.1109/CSO.2011.292
Filename :
5957605
Link To Document :
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