{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:44:04Z","timestamp":1760222644378,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2011,12,20]],"date-time":"2011-12-20T00:00:00Z","timestamp":1324339200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The scope of this paper is twofold. First, we use the Kolmogorov-Sinai Entropy to estimate lower bounds for dominant eigenvalues of nonnegative matrices. The lower bound is better than the Rayleigh quotient. Second, we use this estimate to give a nontrivial lower bound for the gaps of dominant eigenvalues of A and A + V.<\/jats:p>","DOI":"10.3390\/e13122036","type":"journal-article","created":{"date-parts":[[2011,12,20]],"date-time":"2011-12-20T16:40:37Z","timestamp":1324399237000},"page":"2036-2048","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Eigenvalue Estimates Using the Kolmogorov-Sinai Entropy"],"prefix":"10.3390","volume":"13","author":[{"given":"Shih-Feng","family":"Shieh","sequence":"first","affiliation":[{"name":"Department of Mathematics, National Taiwan Normal University, 88 SEC. 4, Ting Chou Road, Taipei 11677, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2011,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1137\/0609004","article-title":"On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications","volume":"9","author":"Arbenz","year":"1988","journal-title":"SIAM J. 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Chaos Appl. Sci. Engrg."},{"key":"ref_6","first-page":"861","article-title":"A new metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces","volume":"119","author":"Kolmogorov","year":"1958","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"ref_7","first-page":"754","article-title":"On the entropy per time unit as a metric invariant of auto-morphisms","volume":"21","author":"Kolmogorov","year":"1958","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ma\u00f1\u00e9, R. (1987). Ergodic Theory and Differentiable Dynamics, Springer-Verlag.","DOI":"10.1007\/978-3-642-70335-5"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1090\/S0002-9947-1964-0161372-1","article-title":"Intrinsic Markov chains","volume":"112","author":"Parry","year":"1964","journal-title":"Trans. Amer. Math. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"082701","DOI":"10.1063\/1.2203229","article-title":"Mathematical analysis of the wavelet method of chaos control","volume":"47","author":"Shieh","year":"2006","journal-title":"J. Math. Phys."},{"key":"ref_11","unstructured":"Stewart, G.W., and Sun, J.-G. (1990). Matrix Perturbation Theory, Academic Press."},{"key":"ref_12","unstructured":"Wheeden, R.L., and Zygmund, A. (1977). Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/13\/12\/2036\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:58:25Z","timestamp":1760219905000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/13\/12\/2036"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,20]]},"references-count":12,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2011,12]]}},"alternative-id":["e13122036"],"URL":"https:\/\/doi.org\/10.3390\/e13122036","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2011,12,20]]}}}