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A note on the perturbation of positive matrices by normal and unitary matrices

โœ Scribed by Michael Neumann; Nung-Sing Sze


Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
103 KB
Volume
428
Category
Article
ISSN
0024-3795

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helmut wielandt zum 90. geburtstag Let A and B be stochastic matrices of the same type n n . It is natural to consider perturbations A t of A of the form Now, the following two questions come up immediately. (1) When does lim kโ†’โˆž A t k exist? (2) How does lim kโ†’โˆž A t k behave for small t? As the

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โœ Chi-Kwong Li; Ren-Cang Li ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 183 KB

be Hermitian matrices with eigenvalues ฮป 1 โ€ข โ€ข โ€ข ฮป k and ฮป 1 โ€ข โ€ข โ€ข ฮป k , respectively. Denote by E the spectral norm of the matrix E, and ฮท the spectral gap between the spectra of H 1 and H 2 . It is shown that , which improves all the existing results. Similar bounds are obtained for singular valu