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作 者:陈雨 陈建龙 Chen Yu;Chen Jianlong(School of Mathematics,Southeast University,Nanjing,Jiangsu 210096)
机构地区:[1]东南大学数学学院,南京210096
出 处:《高等学校计算数学学报》2021年第3期220-231,共12页Numerical Mathematics A Journal of Chinese Universities
基 金:国家自然科学基金的支持(No.11771076,11871145).
摘 要:1引言本文中,C^(m×n)代表复数域C上的所有m×n阶矩阵的集合.对A∈C^(m×n),A*、R(A)、N(A)、rank(A)分别代表A的共轭转置、列空间、零空间、秩.使得rank(A^(k))=rank(A^(k+1))成立的最小正整数k称为A的指标,记作ind(A).The Moore-Penrose inverse is a type of classical generalized inverses.There have been relatively complete results about Moore-Penrose inverses of complex matrices,bounded linear operators in Hilbert spaces,elements in rings and morphisms in categories.The weighted Moore-Penrose inverse,as a generalization of the Moore-Penrose inverse,has a wider range of applications.In recent years,the weighted Moore-Penrose inverse theory has developed rapidly,playing an increasingly important role in theoretical research and applied research.This paper introduces some progress of weighted Moore-Penrose inverses when the weights are positive definite Hermitian,invertible Hermitian,and invertible,respectively.
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