线性代数中行列式的降阶方法  

Order Reduction of Determinants in Linear Algebra

作　　者：徐运阁 陈媛 XU Yunge;CHEN Yuan(Faculty of Mathematics and Statistics,Hubei Key Laboratory of Applied Mathematics,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学数学与统计学学院应用数学湖北省重点实验室

出　　处：《高等数学研究》2020年第1期97-101,共5页Studies in College Mathematics

基　　金：湖北省教育厅教研项目(2017234)

摘　　要：本文归纳线性代数中关于行列式的常用降阶方法,通过摄动法将这些降阶公式由子矩阵块的可逆情形推广到一般情形,并基于矩阵的满秩分解,给出降阶公式的使用技巧.This paper summarizes commonly used order reduction formulae for determinants in linear algebra.By the method of perturbation,the case of invertible submatrix blocks in reduced-order formulae is generalized to the general case.Based on the full-rank decomposition of matrices,some skills of using these reduced-order formulae are given.

关 键 词：行列式 降阶 满秩分解 线性代数 

分 类 号：O151.2[理学—数学]