包含切比雪夫多项式的循环矩阵行列式的计算

行首加r尾r右循环矩阵和行尾加r首r左循环矩阵是两种特殊类型的矩阵,这篇论文中就是利用多项式因式分解的逆变换这一重要的技巧以及这类循环矩阵漂亮的结构和切比雪夫多项式的特殊的结构,分别讨论了第一类、第二类切比雪夫多项式的关于行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式,从而给出了行首加r尾r右循环矩阵和行尾加r首r左循环矩阵的行列式显式表达式.这些显式表达式与切比雪夫多项式以及参数r有关.这一问题的应用背景主要在循环编码,图像处理等信息理论方面.

Determinants of RFPrLrR circulant matrices of the Chebyshev polynomials

In this paper, two new kind of circulant matrices, i.e., the RFPrLrR circulant matrix and the RLPrFrL circulant matrix over the complex field C are considered respectively. The determinants of RFPrLrR circulant matrices and RLPrFrL circulant matrices of the Chebyshev polynomials are given by using the inverse factorization of polynomial. The calculation problem of a class determinant involving Chebyshev Polynomials are solved by using the combinatorial method and algebraic manipulations .