Spectrum and eigenvectors for a class of tridiagonal matrices

Chu, Wenchang

doi:10.1016/j.laa.2019.08.017

Cited by 13 publications

(7 citation statements)

References 16 publications

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“…With the above assumptions, this inverse problem is known to have one unique solution [5,6]. Analogous results are known for eigenvalues in a linear sequence [7,8], λ k ∝ k, a case relevant to the study of quantum-state transfer [9], as well as in other cases [10][11][12].…”

Section: Resultsmentioning

confidence: 93%

Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains

Vaia

Spadini

2020

Linear Algebra and its Applications

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A real persymmetric Jacobi matrix of order n whose eigenvalues are 2k 2 n−1 k=0 is presented, with entries given as explicit functions of n. Besides the possible use for testing forward and inverse numerical algorithms, such a matrix is especially relevant for its connection with the dynamics of a mass-spring chain, which is a multi-purpose prototype model. Indeed, the mode frequencies being the square roots of the eigenvalues of the interaction matrix, one can shape the chain in such a way that its dynamics be perfectly periodic and dispersionless.

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Section: Resultsmentioning

confidence: 93%

Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains

Vaia

Spadini

2020

Linear Algebra and its Applications

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“…The Sylvester-Kac matrix was first introduced by James J. Sylvester in 1854 [8], then research conducted by Kac found the determinant of the matrix. Some of the developments carried out by W. Chu, et al [2], [3], [4] then R. Bevilaqua, et al [1], C.M. da Fonseca, E. Kilic [5], [6] and by Z. Jiang, et al [7] regarding the Sylvester-Kac matrix both spectrum, determinant and inverse search.…”

Section: Introduction and Premilinariesmentioning

confidence: 99%

Determinant and inverse of T-Sequence-Sylvester-Kac Matrix

Saputra

Amir²,

Anwar³

2023

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The Sylvester-Kac matrix is also known as the Clement matrix The Sylvester-Kac matrix is widely used and applied both in processing, graphs and other fields. The Sylvester-Kac matrix developed in the paper is the T-Sequence-Sylvester-Kac matrix The calculation of the determinant, and inverse has always been a challenge for mathematicians to find. In this paper will be given the formulation of determinant, and inverse of the T-Sequence-Sylvester-Kac matrix

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“…One particular case whose determinant evaluation was conjectured (without proof) by Sylvester [19, page 305] is where the matrix entries are given by For this elegant result, there exist a number of generalisations and applications (see, for example, [2, 4, 9–11, 14–16, 20]). However, eigenvectors have only been found for a few related tridiagonal matrices (see [3, 6, 7, 12]).…”

Section: Introductionmentioning

confidence: 99%

“…The paper is organised as follows. In the next section, the eigenvectors of are determined explicitly by following the same approach as in [6]. In Section 3, we prove orthogonality relations between the left and right eigenvectors.…”

Section: Introductionmentioning

confidence: 99%