Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix
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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.