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