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arXiv · 1910.01379

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

Ruggero Vaia·Lidia Spadini
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Abstract

A real persymmetric Jacobi matrix of order $n$ whose eigenvalues are $2k^2$ $(k=0, ..., n-1)$ 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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BibTeXRIS

Ruggero Vaia, Lidia Spadini. 2019-10-03. Persymmetric Jacobi matrices with square-integer eigenvalues and dispersionless mass-spring chains. https://doi.org/10.1016/j.laa.2019.10.002

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