两类矩阵多项式的逆矩阵的求法

The inverse calculation of two types of matrix polynomials

矩阵的求逆是矩阵论中研究的重要问题,尤其是一些矩阵多项式的求逆问题.在求矩阵多项式的逆矩阵过程中,研究发现一些特殊矩阵多项式与其逆之间不仅有密切联系,而且有特殊的结构或形式.文中对两类矩阵多项式的逆矩阵求法进行了探讨,研究求逆的一些方法,得出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.对丰富矩阵多项式的求逆理论具有重要意义,对学习求逆知识也具有借鉴作用.

The inverse calculation of matrix is an important problem in matrix theory, particularly the problem of the inversion of matrix polynomials. It is found that there are not only close ties but also special structures or forms between several kinds of special matrix and their inverse matrix. In the paper, inverse matrices solving methods of two classes of matrix polynomials are discussed to draw the formula of inverse matrices polynomials, and to put the results into real use. This study has certain important significance for solving relevant problems and the conclusion of it is also a good reference to further study of the inversion calculation of matrix polynomials.