We derive bounds on the moduli of the eigenvalues of special type of rational matrices using the following techniques/methods: (1) the Bauer-Fike theorem on an associated block matrix of the given rational matrix, (2) by associating a real rational function, along with Rouch$\text{\'e}$ theorem for the rational matrix and (3) by a numerical radius inequality for a block matrix for the rational matrix. These bounds are compared when the coefficients are unitary matrices. Numerical examples are given to illustrate the results obtained.

翻译：本文通过以下技术/方法推导了特殊类型有理矩阵特征值模的界：(1) 对给定有理矩阵的关联分块矩阵应用Bauer-Fike定理，(2) 通过关联实有理函数并结合有理矩阵的Rouché定理，(3) 利用有理矩阵分块矩阵的数值半径不等式。在系数为酉矩阵的情形下比较了这些界。文中给出了数值算例以说明所得结果。