We consider a minimal realization of a rational matrix functions. We perturb the polynomial part and one of the constant matrices from the realization part. We derive explicit computable expressions of backward errors of approximate eigenvalue of rational matrix function. We also determine minimal perturbations for which approximate eigenvalue are exact eigenvalue of the perturbed matrix rational functions.

翻译：我们认为最起码实现合理的矩阵函数。 我们从实现部分中扰动多元部分和恒定矩阵之一。 我们从理性矩阵函数的近乎等值的后向错误中得出明确的可计算表达法。 我们还确定了最微小的扰动,其中约近于等值的扰动是扰动矩阵合理函数的精度值。