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一类2×2分块矩阵的Drazin逆

发表时间:2009-07-15  浏览量:1665  下载量:517
全部作者: 刘喜富,杨虎
作者单位: 重庆大学数理学院
摘 要: 讨论了一类特殊的四分块矩阵的Drazin逆——当块矩阵A是一个幂等矩阵的情况下三角矩阵M的Drazin逆。主要通过2种矩阵分解方式对M进行分解:一是对矩阵M进行块分解和行列变换,把矩阵M转化成一个便于求解其Drazin逆表达式的分块矩阵;二是将矩阵M分解成2个矩阵的乘积,然后利用矩阵乘积的Drazin逆计算公式计算M的Drazin逆表达式。并在新条件下,给出矩阵M的Drazin逆的表达式,推广并补充了这方面的研究成果。
关 键 词: 代数学;Drazin逆;分块矩阵;指数;秩
Title: Drazin inverse for a class of 2� block matrices
Author: LIU Xifu, YANG Hu
Organization: College of Mathematics and Physics, Chongqing University
Abstract: This paper discusses the Drazin inverse of a special 2� block matrices: the Drazin inverse of the triangular matrix M when A is idempotent. Two main methods of matrix factorization are used to obtain the representation of the Drazin inverse of M: one is using the methods of block factorization and row and column transposition on M, then transforms M to a block matrix so that its representation for the Drazin inverse can be easily obtained; and another is decomposing M into the product of two matrices, then applies the formula of the Drazin inverse of the product of two matrices to compute the Drazin inverse of M. Under some new conditions, the results extend some known results on Drazin inverse.
Key words: algebra; Drazin inverse; block matrices; index; rank
发表期数: 2009年7月第13期
引用格式: 刘喜富,杨虎. 一类2×2分块矩阵的Drazin逆[J]. 中国科技论文在线精品论文,2009,2(13):1337-1340.
 
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