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

Alexander Dyachenko; Mikhail Tyaglov

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2109.10771 v2 pith:COQCSA6S submitted 2021-09-22 math.SP

Alexander Dyachenko , Mikhail Tyaglov This is my paper · ORCID

classification math.SP

keywords maindiagonalmatrixspectrumeigenvectorstridiagonaltwo-periodicarbitrary

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original 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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Squeezed states for Frenkel-like two-fermion composite bosons
quant-ph 2025-12 conditional novelty 5.0 of 10

Squeezed Frenkel-like cobosons, defined as eigenstates of a Bogoliubov-transformed coboson operator, have uncertainty product (1−⟨D⟩)/2, dropping below canonical 1/2 due to Pauli blocking.

Pith tools