Eigenvalues for tridiagonal 3-Toeplitz matrices

Document Type : Research Paper


Department of Applied Mathematics, Payame Noor University, Po Box 19395-3697 Tehran, Iran.


In this paper, we study the eigenvalues of real tridiagonal 3-Toeplitz matrices
of different order. When the order of a tridiagonal 3-Toeplitz matrix is n = 3k + 2,
the eigenvalues were found explicitly. Here, we consider the distribution of eigenvalues
for a tridiagonal 3-Toeplitz matrix of orders n = 3k and n = 3k + 1. We explain our
method by finding roots of a combination of Chebyshev polynomials of the second
kind. This distribution solves the eigenproblem for integer powers of such matrices.


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Volume 10, Issue 2
Special Issue Dedicated to Professor M. Radjabalipour on the occasion of his 75th birthday.
October 2021
Pages 63-72
  • Receive Date: 29 March 2021
  • Revise Date: 31 July 2021
  • Accept Date: 26 August 2021