Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix

Abstract

The Sylvester matrix was first defined by JJ Sylvester. Some authors have studied the relationships between certain orthogonal polynomials and the determinant of the Sylvester matrix. Chu studied a generalization of the Sylvester matrix. In this paper, we introduce its $2$-periodic generalization. Then we compute its spectrum by left eigenvectors with a similarity trick.