×

Lower bounds for the spread of a Hermitian matrix. (English) Zbl 0886.15017

The authors present new lower bounds for the spread of a Hermitian matrix in terms of its entries. The results include a bound which is sharper than a recent result due to E. R. Barnes and A. J. Hoffman [Linear Algebra Appl. 201, 79-90 (1994; Zbl 0803.15016)] in spite of the fact that the latter bound is attained. Numerical examples are used to compare the results with other known results.
Reviewer: Z.Dostal (Ostrava)

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
15B57 Hermitian, skew-Hermitian, and related matrices

Citations:

Zbl 0803.15016
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barnes, E. R.; Hoffman, A. J., Bounds for the spectrum of normal matrices, Linear Algebra Appl., 201, 79-90 (1994) · Zbl 0803.15016
[2] Finke, G.; Burkard, R. E.; Rendl, F., Quadratic assignment problems, Ann. Discrete Math., 31, 61-82 (1987)
[3] Johnson, C. R.; Kumar, R.; Wolkowicz, H., Lower bounds for the spread of a matrix, Linear Algebra Appl., 71, 161-173 (1985) · Zbl 0578.15013
[4] Mirsky, L., Inequalities for normal and Hermitian matrices, Duke Math. J., 24, 591-598 (1957) · Zbl 0081.25101
[5] Scott, D. S., On the accuracy of the Gerschgorin circle theorem for bounding the spread of a real symmetric matrix, Linear Algebra Appl., 65, 147-155 (1985) · Zbl 0589.15012
[6] Stewart, G. W.; Sun, J.-G., Matrix Perturbation Theory (1990), Academic
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.