Spectra of Nearly Hermitian Matrices

W. Kahan
1975 Proceedings of the American Mathematical Society  
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. h +2.038) ||ß||; moreover, for all n > 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 1 -2 --n ' J rJ J
doi:10.2307/2040683 fatcat:oqcep463bjhr7bwhom64oq2fee