矩阵分块的一点应用

Application of Partitioning of a Matrix

通过矩阵的适当分块,并借助于矩阵的相关知识,得到了高阶矩阵的秩、行列式以及逆与低阶矩阵相应量之间的关系,从而把高阶矩阵的秩、行列式及逆的问题转化为低阶矩阵的相应问题来处理,为计算机处理高阶矩阵问题提供简化算法。同时,所得结论极大简化了系统理论一些已有的重要结论的证明,最后给出具体的算例以证实方法的有效性。

In this paper,by using appropriate partitioning of matrices and related theory of matrix,some practicable equalities on rank,determinant,and the inverse of a matrix between higher order and lower order are presented.These equalities provide some simplified algorithms for handling higher order matrix via the computer.Based on the proposed results,some important theorems can be proved more easily.Finally,the numerical example is given to verify the effectiveness of the proposed results.