几类特殊矩阵求逆矩阵的方法研究

Methods Study of Several Kinds of Special Matrices in Inverse Matrix Aspect

随着科学技术和生产的不断发展,矩阵的应用更加广泛,而可逆矩阵在矩阵理论中一直占有很重要的地位.本文重点针对一些在教材中不常碰到,而实际生活中应用广泛的矩阵,如:n阶循环矩阵,整数环矩阵,复数矩阵,根据判别矩阵可逆常用方法及特殊矩阵的基本性质,给出判断这些矩阵是否可逆的判定方法及相应逆矩阵的求法.

With the development of science and technology and production, Matrix is more widely used, and the invertible matrix has always been very important in matrix theory. On the basis of mastering the common methods of discriminant matrices, this paper is going to focus on some of those which are rarely seen in the textbook, but widely applied in real life , Such as n - order cyclic matrix, the integer ring matrix, Complex matrix, elaborating its definition , basic properties, and giving the common ways to determine if these matrices are reversible , and then a better understanding of how to distinguish the reversibility of these special matrix will be realized .