Kh. D. Ikramov, “On a Remarkable Property of a Matrix of Mark Kac”, Mat. Zametki, 72:3 (2002), 356–362; Math. Notes, 72:3 (2002), 325

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Matematicheskie Zametki, 2002, Volume 72, Issue 3, Pages 356–362
DOI: https://doi.org/10.4213/mzm427 (Mi mzm427)

This article is cited in 10 scientific papers (total in 10 papers)

On a Remarkable Property of a Matrix of Mark Kac

Kh. D. Ikramov

M. V. Lomonosov Moscow State University

Full-text PDF (151 kB) Citations (10)

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DOI: https://doi.org/10.4213/mzm427

Abstract: A triangular submatrix extracted in a special way from the Mark Kac matrix has a remarkable spectral property: if the order of its columns is reversed, then half of the eigenvalues do not change, whereas the other half are multiplied by -1. This fact discovered by this author somewhat earlier has had no explanation until now. Such an explanation is given in this paper.

Received: 19.09.2001

English version:
Mathematical Notes, 2002, Volume 72, Issue 3, Pages 325–330
DOI: https://doi.org/10.1023/A:1020543219652

Bibliographic databases:

UDC: 519.6

Language: Russian

Citation: Kh. D. Ikramov, “On a Remarkable Property of a Matrix of Mark Kac”, Mat. Zametki, 72:3 (2002), 356–362; Math. Notes, 72:3 (2002), 325–330

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm427

https://doi.org/10.4213/mzm427

https://www.mathnet.ru/eng/mzm/v72/i3/p356

This publication is cited in the following 10 articles:

WENCHANG CHU, EMRAH KILIÇ, “LEFT AND RIGHT EIGENVECTORS OF A VARIANT OF THE SYLVESTER–KAC MATRIX”, Bull. Aust. Math. Soc., 109:2 (2024), 316
Abdullah Alazemi, Tim Hopkins, Emrah K{\i}lıç, “A four parameter extension to the Clement matrix and its role in numerical software testing”, Journal of Computational and Applied Mathematics, 450 (2024), 115986
Zhibin Du, Carlos M. da Fonseca, “Sylvester–Kac matrices with quadratic spectra: A comprehensive note”, Ramanujan J, 2024
Zhibin Du, Carlos M. da Fonseca, “A note on the eigenvalues of a Sylvester–Kac type matrix with off-diagonal biperiodic perturbations”, Journal of Computational and Applied Mathematics, 2024, 116429
da Fonseca C.M., Kilic E., “A New Type of Sylvester-Kac Matrix and Its Spectrum”, Linear Multilinear Algebra, 69:6 (2021), 1072–1082
Da Fonseca C.M., Kilic E., Pereira A., “The Interesting Spectral Interlacing Property For a Certain Tridiagonal Matrix”, Electron. J. Linear Algebra, 36 (2020), 587–598
da Fonseca C.M., Kilic E., “An Observation on the Determinant of a Sylvester-Kac Type Matrix”, Analele Stiint. Univ. Ovidius C., 28:1 (2020), 111–115
da Fonseca C.M., “A Short Note on the Determinant of a Sylvester-Kac Type Matrix”, Int. J. Nonlinear Sci. Numer. Simul., 21:3-4 (2020), 361–362
Chu W., “Spectrum and Eigenvectors For a Class of Tridiagonal Matrices”, Linear Alg. Appl., 582 (2019), 499–516
da Fonseca C.M., Mazilu D.A., Mazilu I., Williams H.T., “The Eigenpairs of a Sylvester-Kac Type Matrix Associated with a Simple Model for One-Dimensional Deposition and Evaporation”, Appl. Math. Lett., 26:12 (2013), 1206–1211

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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