Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix
Copyright policy )Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix
Summary: 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. In [Calcolo 45, No. 4, 217--233 (2008; Zbl 1175.15010)], \textit{W. Chu} and \textit{X. Wang} 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.
Eigenvalues, singular values, and eigenvectors, Sylvester matrix, Determinants, permanents, traces, other special matrix functions, determinant, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), spectrum
Eigenvalues, singular values, and eigenvectors, Sylvester matrix, Determinants, permanents, traces, other special matrix functions, determinant, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), spectrum
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