矩阵分块的一般办法

On Matrix Partition

本文对矩阵的行向量和列向量集合进行极端情况下划分,得到了对矩阵的行、列向量集合进行最粗划分和最细划分下,有8种组合划分的方法.然后运用矩阵与线性映射的刻画关系,利用本文提出的分块办法解决线性映射复合运算下向量元素的坐标变换问题.

This paper explores the partition of row vectors and column vectors of a matrix under extreme circumstances,and obtains 8 partition methods under the coarsest partition and the smallest partition of row and column vectors.Using the relationship between matrix and linear mapping and the blocking method,the coordinate transformation problem under the compounded linear mappings is solved.