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Curves and envelopes that bound the spectrum of a matrix
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 557Article in journal (Refereed) Published
Abstract [en]

A generalization of the method developed by Adam, Psarrakos and Tsatsomeros to find inequalities for the eigenvalues of a complex matrix A using knowledge of the largest eigenvalues of its Hermitian part H(A) is presented. The numerical range or field of values of A can be constructed as the intersection of half-planes determined by the largest eigenvalue of H(e(i theta) A.). Adam, Psarrakos and Tsatsomeros showed that using the two largest eigenvalues of H(A), the eigenvalues of A satisfy a cubic inequality and the envelope of such cubic curves defines a region in the complex plane smaller than the numerical range but still containing the spectrum of A. Here it is shown how using the three largest eigenvalues of H(A) or more, one obtains new inequalities for the eigenvalues of A and new envelope-type regions containing the spectrum of A. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE INC , 2018. Vol. 557
Keywords [en]
Spectrum localization; Eigenvalue inequalities; Envelope; Numerical range
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-151761DOI: 10.1016/j.laa.2018.07.025ISI: 000444926700001OAI: oai:DiVA.org:liu-151761DiVA, id: diva2:1254181
Available from: 2018-10-08 Created: 2018-10-08 Last updated: 2019-03-18

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The full text will be freely available from 2020-07-24 14:59
Available from 2020-07-24 14:59

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Bergqvist, Göran
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