The Sylvester–Kac matrix, also known as Clement matrix, has many extensions and applications. The evaluation of determinant and spectra of many of its generalizations sometimes are hard to compute. Recently, E. Kılıç and T. Arikan proposed an extension the Sylvester–Kac matrix, where the main diagonal is a 2-periodic sequence. They found its determinant using a spectral technique. In this short note, we provide a simple proof for that result by calculating directly the determinant.

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关于Sylvester–Kac类型矩阵行列式的简短说明

Sylvester-Kac矩阵，也称为Clement矩阵，具有许多扩展和应用。有时很难计算行列式和许多泛化谱的评估。最近，E。Kılıç和T. Arikan提出了Sylvester-Kac矩阵的扩展，其中主对角线是2周期序列。他们使用光谱技术找到了决定因素。在本简短说明中，我们通过直接计算行列式来为该结果提供简单证明。