摘要：矩阵是线性代数的重要组成部分，也是数学许多分支研究和应用的重要工具.对于阶数比较高的矩阵,为了计算方便且显现出矩阵的局部特征，我们常用分块矩阵来进行讨论和运算.分块矩阵是矩阵的一种推广，一般矩阵的元素是数量，而分块矩阵的元素可以是数量，也可以是矩阵.本文总结分块矩阵行列式计算方面的相关性质，并应用其解决某些行列式计算问题.

关键字：分块初等矩阵；分块矩阵；行列式；应用

Abstract：Matrix is the very important component of linear algebra, but also very important tool in the research and application of many branches of mathematics. When the order of matrix is high, we use the block matrix to discuss and calculate in order to show the features of matrix and make the calculation conveniently. Block matrix is a promotion of matrix. While the general element of matrix is number, the element of block matrix can be a number or a matrix. The introduction of block matrix makes matrix an effective shortcut for complicated determinant .This paper summarizes some related natures in the calculation. Also it uses the nature to solve some problems in the calculation of determinant.

Keywords: block-elementary matrix; block matrix; determinant; application