Spectra of Nearly Hermitian Matrices.
Abstract
When properly ordered, the respective eigenvalues of an n x n Hermitian matrix A and of a nearby non-Hermitian matrix A + B cannot differ by more than ((log of n to the base 2) + 2.038)//B//; moreover, for n > or = 4 examples A and B exist for which this bound is in excess by at most about a factor 3. This bound is contrasted with other previously published over-estimates that appear to be independent of n. Further, a bound is found, for the sum of the squares of respective differences between the eigenvalues, that resembles the Hoffman-Wielandt bound which would be valid if A + B were normal. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1974
- Accession Number
- AD0774123
Entities
People
- W. Kahan
Organizations
- University of California, Berkeley