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.
Sylvester matrix, spectrum, determinant
KILIÇ, EMRAH and ARIKAN, TALHA
"Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix,"
Turkish Journal of Mathematics: Vol. 40:
1, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss1/7