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On the spectrum of the tridiagonal matrices with two-periodic main diagonal

Spectral Theory 2022-12-06 v2

Abstract

We find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal provided that the spectrum and eigenvectors of the matrix with the same sub- and superdiagonals and zero main diagonal is known. Our result substantially generalises some recent results on the Sylvester-Kac matrix and its certain main principal submatrices.

Keywords

Cite

@article{arxiv.2109.10771,
  title  = {On the spectrum of the tridiagonal matrices with two-periodic main diagonal},
  author = {Alexander Dyachenko and Mikhail Tyaglov},
  journal= {arXiv preprint arXiv:2109.10771},
  year   = {2022}
}

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9 pages