Upper and lower bounds on absolute values of the eigenvalues of a matrix polynomial are well studied in the literature. As a continuation of this we derive, in this manuscript, bounds on absolute values of the eigenvalues of matrix rational functions using the following techniques/methods: the Bauer-Fike theorem, a Rouch$\text{\'e}$ theorem for matrix-valued functions and by associating a real rational function to the matrix rational function. Bounds are also obtained by converting the matrix rational function to a matrix polynomial. Comparison of these bounds when the coefficients are unitary matrices are brought out. Numerical calculations on a known problem are also verified.

翻译：在文献中,对矩阵多元值绝对值的上下界限进行了充分研究。作为这一定义的延续,我们在本手稿中利用下列技术/方法得出矩阵理性函数的外值绝对值:Bauer-Fike定理仪、用于矩阵价值函数的Rouch$\text=e}元理论,以及将一个真正的理性函数与矩阵理性函数挂钩。还将矩阵理性函数转换成矩阵多元函数,从而获得曲线。当系数为单一矩阵时,对这些界限的比较也得到验证。对已知问题的数值计算也得到验证。