Accession Number : AD0774123
Title : Spectra of Nearly Hermitian Matrices.
Descriptive Note : Final rept.,
Corporate Author : CALIFORNIA UNIV BERKELEY ELECTRONICS RESEARCH LAB
Personal Author(s) : Kahan,W.
Report Date : JAN 1974
Pagination or Media Count : 14
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)
Descriptors : *Matrices(Mathematics), Inequalities, Eigenvectors
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE