Mersin, Efruz ÖzlemBahşi, Mustafa2025-07-242025-07-2420251310-5132 / 2367-8275https://dx.doi.org/10.7546/nntdm.2025.31.2.211-227https://hdl.handle.net/20.500.12451/13554The Sylvester-Kac matrix, a well-known tridiagonal matrix, has been extensively studied for over a century, with various generalizations explored in the literature. This paper introduces a new type of tridiagonal matrix, where the matrix entries are defined by an integer sequence, setting it apart from the classical Sylvester-Kac matrix. The aim of this paper is to investigate several fundamental properties of this generalized matrix, including its algebraic structure, determinant, inverse, LU decomposition, characteristic polynomial, and various norms.eninfo:eu-repo/semantics/closedAccessCharacteristic PolynomialDeterminantNormSylvester–Kac MatrixTridiagonal MatrixArticle31221122710.7546/nntdm.2025.31.2.211-227WOS:001515308200001Q3