You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Spectra of Nearly Hermitian Matrices
Proceedings of the American Mathematical Society
Vol. 48, No. 1 (Mar., 1975), pp. 11-17
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040683
Page Count: 7
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
When properly ordered, the respective eigenvalues of an n × n Hermitian matrix A and of a nearby non-Hermitian matrix A + B cannot differ by more than (log2 n + 2.038) |B|; 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 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.
Proceedings of the American Mathematical Society © 1975 American Mathematical Society