On a conjecture about a tridiagonal matrix

Abstract

In this note we answer to a recent conjecture posed by Q.M. Al-Hassan on a factorization for the characteristic polynomial of the tridiagonal matrix with zero main diagonal and all 1’s sub- and super-diagonals. We recall some less known results in the literature.

Subject Classification: [2010]:

• 15A18
• 15B05

Keywords:

• Characteristic polynomial
• Eigenvalues
• Chebyshev polynomials of second kind