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Relevant bibliographies by topics / Eigenvalue multiplicities

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Academic literature on the topic 'Eigenvalue multiplicities'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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Journal articles on the topic "Eigenvalue multiplicities"

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Johnson, Charles R., Brenda Kroschel, and Matjaž Omladič. "Eigenvalue multiplicities in principal submatrices." Linear Algebra and its Applications 390 (October 2004): 111–20. http://dx.doi.org/10.1016/j.laa.2004.04.019.

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2

Toyonaga, Kenji, and Charles R. Johnson. "The classification of edges and the change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the change in an edge value." Special Matrices 5, no. 1 (2017): 51–60. http://dx.doi.org/10.1515/spma-2017-0004.

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Abstract We take as given a real symmetric matrix A, whose graph is a tree T, and the eigenvalues of A, with their multiplicities. Each edge of T may then be classified in one of four categories, based upon the change in multiplicity of a particular eigenvalue, when the edge is removed (i.e. the corresponding entry of A is replaced by 0).We show a necessary and suficient condition for each possible classification of an edge. A special relationship is observed among 2-Parter edges, Parter edges and singly Parter vertices. Then, we investigate the change in multiplicity of an eigenvalue based up

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3

Kong, Q., H. Wu, and A. Zettl. "Geometric aspects of Sturm—Liouville problems I. Structures on spaces of boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 3 (2000): 561–89. http://dx.doi.org/10.1017/s0308210500000305.

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We consider some geometric aspects of regular Sturm—Liouville problems. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of Sturm—Liouville eigenvalues on the boundary condition, and reveals many new properties of these eigenvalues. In particular, the eigenvalues for separated boundary conditions and those for coupled boundary conditions, or the eigenvalues for self-adjoint boundary conditions and those for non-self-adjoint boundary conditions, are closely related under this structure. Then we give compl

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4

YAN, JUN, and GUOLIANG SHI. "MULTIPLICITIES OF EIGENVALUES OF THE DIFFUSION OPERATOR WITH RANDOM JUMPS FROM THE BOUNDARY." Bulletin of the Australian Mathematical Society 99, no. 1 (2018): 101–13. http://dx.doi.org/10.1017/s0004972718001120.

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This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a zero of the characteristic function $\unicode[STIX]{x1D6E5}(\unicode[STIX]{x1D706})$. This is a new criterion for determining the multiplicities of eigenvalues for concrete operators.

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Johnson, Charles R., and Brian D. Sutton. "Hermitian Matrices, Eigenvalue Multiplicities, and Eigenvector Components." SIAM Journal on Matrix Analysis and Applications 26, no. 2 (2004): 390–99. http://dx.doi.org/10.1137/s0895479802413649.

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Dai, Meifeng, Tingting Ju, Jingyi Liu, Yu Sun, Xiangmei Song, and Weiyi Su. "Applications of Laplacian spectrum for the weighted scale-free network with a weight factor." International Journal of Modern Physics B 32, no. 32 (2018): 1850353. http://dx.doi.org/10.1142/s0217979218503538.

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Laplacian spectrum gives a lot of useful information about complex structural properties and relevant dynamical aspects, which has attracted the attention of mathematicians. We introduced the weighted scale-free network inspired by the binary scale-free network. First, the weighted scale-free network with a weight factor is constructed by an iterative way. In the next step, we use the definition of eigenvalue and eigenvector to obtain the recursive relationship of its eigenvalues and multiplicities at two successive generations. Through analysis of eigenvalues of transition weight matrix we fi

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Marsli, Rachid, and Frank Hall. "On the Location of Eigenvalues of Real Matrices." Electronic Journal of Linear Algebra 32 (February 6, 2017): 357–64. http://dx.doi.org/10.13001/1081-3810.3544.

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The research in this paper is motivated by a recent work of I. Barany and J. Solymosi [I. Barany and J. Solymosi. Gershgorin disks for multiple eigenvalues of non-negative matrices. Preprint arXiv no. 1609.07439, 2016.] about the location of eigenvalues of nonnegative matrices with geometric multiplicity higher than one. In particular, an answer to a question posed by Barany and Solymosi, about how the location of the eigenvalues can be improved in terms of their geometric multiplicities is obtained. New inclusion sets for the eigenvalues of a real square matrix, called Ger\v{s}gorin discs of

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Engman, Martin. "The Spectrum and Isometric Embeddings of Surfaces of Revolution." Canadian Mathematical Bulletin 49, no. 2 (2006): 226–36. http://dx.doi.org/10.4153/cmb-2006-023-7.

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AbstractA sharp upper bound on the first S1 invariant eigenvalue of the Laplacian for S1 invariant metrics on S2 is used to find obstructions to the existence of S1 equivariant isometric embeddings of such metrics in (ℝ3, can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in (ℝ3, can). This leads to generalizations of some classical results in the theory of surfaces.

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9

Wang, Zhong, and Hongyou Wu. "Equality of multiplicities of a Sturm–Liouville eigenvalue." Journal of Mathematical Analysis and Applications 306, no. 2 (2005): 540–47. http://dx.doi.org/10.1016/j.jmaa.2004.10.041.

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von Below, Joachim, and José A. Lubary. "Isospectral infinite graphs and networks and infinite eigenvalue multiplicities." Networks & Heterogeneous Media 4, no. 3 (2009): 453–68. http://dx.doi.org/10.3934/nhm.2009.4.453.

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Dissertations / Theses on the topic "Eigenvalue multiplicities"

1

Gier, Megan E. "EIGENVALUE MULTIPLICITES OF THE HODGE LAPLACIAN ON COEXACT 2-FORMS FOR GENERIC METRICS ON 5-MANIFOLDS." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/14.

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In 1976, Uhlenbeck used transversality theory to show that for certain families of elliptic operators, the property of having only simple eigenvalues is generic. As one application, she proved that on a closed Riemannian manifold, the eigenvalues of the Laplace-Beltrami operator Δg are all simple for a residual set of Cr metrics. In 2012, Enciso and Peralta-Salas established an analogue of Uhlenbeck's theorem for differential forms, showing that on a closed 3-manifold, there exists a residual set of Cr metrics such that the nonzero eigenvalues of the Hodge Laplacian Δg(k) on k-forms are all si

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Books on the topic "Eigenvalue multiplicities"

1

Johnson, Charles R., and Carlos M. Saiago. Eigenvalues, Multiplicities and Graphs. University of Cambridge ESOL Examinations, 2018.

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Book chapters on the topic "Eigenvalue multiplicities"

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Jonker, P., M. Pouw, G. Still, and F. Twilt. "On the partition of real skew-symmetric n × n-matrices according to the multiplicities of their eigenvalues." In Karl der Grosse und sein Nachwirken. 1200 Jahre Kultur und Wissenschaft in Europa. Brepols Publishers, 1998. http://dx.doi.org/10.1484/m.sths-eb.4.2017055.

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Lubary, Jos√©. "On the Geometric and Algebraic Multiplicities for Eigenvalue Problems on Graphs." In Partial Differential Equations On Multistructures. CRC Press, 2001. http://dx.doi.org/10.1201/9780203902196.ch8.

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"On the geometric and algebraic multiplicities for eigenvalue problems on graphs." In Partial Differential Equations On Multistructures. CRC Press, 2001. http://dx.doi.org/10.1201/9780203902196-15.

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Conference papers on the topic "Eigenvalue multiplicities"

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Axell, Erik, and Erik G. Larsson. "A unified framework for GLRT-based spectrum sensing of signals with covariance matrices with known eigenvalue multiplicities." In ICASSP 2011 - 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2011. http://dx.doi.org/10.1109/icassp.2011.5946277.

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