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

Alexander Dyachenko; Mikhail Tyaglov

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arXiv · 2109.10771

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

Alexander Dyachenko·Mikhail Tyaglov

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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.

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BibTeX RIS

Alexander Dyachenko, Mikhail Tyaglov. 2021-09-22. On the spectrum of the tridiagonal matrices with two-periodic main diagonal. https://arxiv.org/abs/2109.10771

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