拉普拉斯定理在行列式计算中的应用  

The Application of Laplace’s Theorem for Determinant Calculation

作　　者：冯依虎 杨星星 FENG Yihu;YANG Xingxing(Department of Electronics and Information Engineering,Bozhou University,Bozhou 236S00,China;Department of Mathematics,Shanghai University,Shanghai 200436,China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800 [2]上海大学数学系,上海200436

出　　处：《忻州师范学院学报》2021年第2期14-17,共4页Journal of Xinzhou Teachers University

基　　金：国家自然科学基金(11271247);安徽省高等学校省级质量工程重点教研项目(2018jyxm0594,2016jyxm0677,2017jyxm0591);亳州学院教学研究重点项目(2017zdjy02)。

摘　　要：行列式展开定理是拉普拉斯定理的特例,拉普拉斯定理是行列式展开定理的推广,利用拉普拉斯定理的推广和证明,对其任意取定的k阶子式进行讨论得到其特例,即为行列式展开定理,运用拉普拉斯定理和行列式性质证明了行列式的乘积,最后将拉普拉斯定理运用到高阶行列式与矩阵行列式的计算中,通过广义对角矩阵行列式进行推广,在分块矩阵行列式计算中进行分类讨论,得到了更一般形式的分块矩阵行列式的计算公式。Determinant theorem is a special case of the Laplace’s theorem,the Laplace’s theorem is an extension of the determinant expansion theorem in this paper,by using Laplace theorem of promotion and prove that the son of arbitrary order k type to discuss its special case,is the determinant theorem,and use the Laplace’s theorem and the determinant nature proved that the product of the determinant,the final will be Laplace theorem is applied to the calculation of higher-order determinant determinant and matrix,the generalized diagonal matrix determinant,classified discussion in the partitioned matrix determinant calculation,got the more general form of partitioned matrix determinant calculation formula.

关 键 词：拉普拉斯定理 行列式展开定理 分块矩阵 代数余子式 

分 类 号：O151.22[理学—数学]