Some comments on the properties of a particular tridiagonal matrix

Abstract

Recently, Q.M. Al-Hassan discussed some properties of the tridiagonal matrix with zero main diagonal and all 1’s sub- and super-diagonals. In this brief note, we show that these properties are special cases of a vast theory involving Chebyshev polynomials of second kind.

Subject Classification: (2000):

• 15A18
• 42C05
• 33C45

Keywords:

• Characteristic polynomial
• Eigenvalues
• Orthogonal polynomials
• Chebyshev polynomials of second kind