分块三角矩阵逆的存在性判定及其计算  

The existence determination and calculation of the inverse of block triangular matrices

作　　者：冯福存[1] 常莉红 金钰[1] FENG Fucun;CHANG Lihong;JIN Yu(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan Ningxia 756099)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756099

出　　处：《宁夏师范学院学报》2024年第7期32-41,共10页Journal of Ningxia Normal University

基　　金：宁夏自然科学基金项目(2022AAC03334,2023AAC03330)。

摘　　要：研究了分块三角矩阵可逆性的判定及其逆矩阵的表示.首先,利用分块初等矩阵的性质给出了分块上(下)三角矩阵的可逆条件及其逆矩阵的表示.然后,利用置换矩阵的性质进一步给出分块次上(下)三角矩阵的可逆条件及其逆矩阵的表示.最后,通过实例对所提计算方法进行验证.The determination of reversibility of block triangular matrices and the representation of inverse matrices are studied.Firstly,using the properties of block elementary matrices,the invertible conditions and inverse matrix representation of block upper(lower)triangular matrices are given.Then,based on the properties of permutation matrices,the invertible conditions and inverse matrix representation of block upper(lower)triangular matrices are obtained.Finally,an example is given to verify the proposed algorithm.

关 键 词：分块初等矩阵 分块置换矩阵 分块三角矩阵 逆矩阵 

分 类 号：O151.21[理学—数学]