巧用多项式的除法求矩阵多项式的逆矩阵

The Solution to Inverse Matrix of Matrix Polynomial by Skillfully Using Polynomial Division

利用多项式的除法技巧,给出了一个求解矩阵多项式的逆矩阵的新方法,得出了两类矩阵多项式的求逆公式,并且对相关结论分别举例加以应用,使得这两类矩阵多项式求逆变得简单明了,相关问题也可以迎刃而解;同时,利用多项式的除法技巧还得到文献[3]中的两个关于矩阵多项式的逆矩阵的结论,对学习求逆具有借鉴作用。

By using polynomial division skill, this paper gives a new method to solve inverse matrix of matrix polynomial, obtains two kinds of the formula to solve the polynomial matrices, applies the related conclusions by taking examples, makes these two kinds of the solutions to the inverse matrices of polynomial matrices simpler and simple to solve the similar problems, meanwhile, uses polynomial division skill to receive two conclusions on the inverse matrix related to polynomial matrices in reference [ 3 ], which is of reference significance to the solution to inverse matrices.