一个矩阵多项式求逆问题的推广

A Generalization of a Matrix Polynomial Inversion

矩阵求逆是高等代数研究的重要问题,建立在此基础上的矩阵多项式求逆问题,因其复杂灵活的形式而成为一个研究难点.从一个二次矩阵多项式的求逆问题出发,运用逆矩阵定义、多项式互素、线性方程组理论给出了该问题的三种解法,并通过第三种方法进一步推得了此类矩阵多项式的求逆公式.

An important study of higher algebra is matrix inversion, on the base of which is matrix polynomial inversion, which is a difficulty because of its complex and changeable forms. Starting from a inversion of quadric matrix polynomial, three resolu- tions are given by.the way of the definition of inverse matrix, polynomial coprime and theory on the linear system of equations and the inverse formula of the polynomial matrix is generalized by the third resolution.