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Matematicheskie Zametki, 2006, Volume 79, Issue 2, Pages 169–177
DOI: https://doi.org/10.4213/mzm2687
(Mi mzm2687)
 

Estimates for the Eigenvalues of Matrices

R. I. Alidemaa, A. F. Filippovb

a University of Prishtina
b M. V. Lomonosov Moscow State University
References:
Abstract: For matrices whose eigenvalues are real (such as Hermitian or real symmetric matrices), we derive simple explicit estimates for the maximal $(\lambda_{\max})$ and the minimal $(\lambda_{\min})$ eigenvalues in terms of determinants of order less than 3. For $3\times3$ matrices, we derive sharper estimates, which use $\det A$ but do not require to solve cubic equations.
Received: 13.09.2004
English version:
Mathematical Notes, 2006, Volume 79, Issue 2, Pages 157–164
DOI: https://doi.org/10.1007/s11006-006-0019-5
Bibliographic databases:
UDC: 519.614.2
Language: Russian
Citation: R. I. Alidema, A. F. Filippov, “Estimates for the Eigenvalues of Matrices”, Mat. Zametki, 79:2 (2006), 169–177; Math. Notes, 79:2 (2006), 157–164
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm2687
  • https://www.mathnet.ru/eng/mzm/v79/i2/p169
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    Математические заметки Mathematical Notes
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