Moore-Penrose Inverse of a Gram Matrix and Its Nonnegativity

Let M=[A  a] be a matrix of order m×n, where A∈ℝ ^m×(n−1) and a∈ℝ ^m is an m×1 vector. In this article, we derive a formula for the Moore-Penrose inverse of M ^* M and obtain sufficient conditions for its nonnegativity. The results presented here generalize the ones known earlier. The authors thank the anonymous referee for suggestions on an earlier version that have resulted in an improved presentation.     

分块矩阵的Moore-Penrose逆

该文研究了两类3×3分块矩阵M1=AOOBCODEF,M2=ABCDEFGHK的Moore-Penrose逆的表达式,并给出了表达式成立时的条件.     

环上矩阵的Moore-Penrose逆

本文研究环上矩阵的广义逆,得到其存在的充要条件,给出它的表达式,推广了以往文献的相应结果。     

Fuzzy矩阵的加权Moore-Penrose逆

给出了Fuzzy矩阵加权Moore-Penrose逆AM+N的定义,研究了Fuzzy矩阵加权Moore-Penrose逆AM+N的存在性问题,证明了当权矩阵M,N满足一定条件时,AM+N存在且A+MN=AT的充要条件是ANATMA≤A,推广了Fuzzy矩阵和Boolean矩阵的相应结果.     

矩阵的加权Moore—Penrose逆

利用矩阵的广义奇异值分解，给出了复数域上矩阵的Moore—Penrose逆存在的充要条件及其表达式．     

Moore-Penrose Inverses and Group Inverses of Block k-Circulant Matrices

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任意Banach空间中线性算子的Moore-Penrose度量广义逆

在无空间严格凸的几何假定下,利用Banach空间几何方法给出了任意Banach空间中线性算子T的Moore-Penrose度量广义逆T~+的存在性、唯一性、极小性和线性性的充要条件,同时还讨论了T~+的一些性质,这些本质地将文献[8]的最近结果从严格凸Banach空间拓广至任意Banach空间．     

Approximation Theorems of Moore-Penrose Inverse by Outer Inverses

1 Introduction and preliminaries Let X and Y be two Hilbert spaces and T a bounded linear operator from X into Y . We use D(T ), N(T ) and R(T ), respectively, to denote the domain, null space and range of T . Recall that a linear operator T # : Y → X is…     

环上矩阵广义Moore-Penrose逆的存在性

讨论带有对合反自同构*有单位元的结合环R上矩阵的广义Moore-Penrose 逆,给出了环R上矩阵的广义Moore-Penrose逆存在的几个充要条件．特别,得到了环 R上矩阵A的关于M和N的广义Moore-Penrose逆存在的充要条件是A有分解A= GDH,其中D2=D,(MD)*=MD,(GD)*MGD+M(I-D)和DHN-1(DH)*+ (I-D)M-1均可逆．     

矩阵的加权Moore-Penrose逆

利用矩阵的广义奇异值分解, 给出了复数域上矩阵的Moore-Penrose逆存在的充要条件及其表达式.     

Moore-Penrose广义逆矩阵与线性方程组的解

线性方程组的逆矩阵求解方法只使用于系数矩阵为可逆方阵,对于一般线性方程组可以应用Moore-Penrose广义逆矩阵来研究并表示其通解,本文主要探讨Moore-Penrose广义逆矩阵及一般线性方程组通解和最小范数解.     

An improved method for the computation of the Moore-Penrose inverse matrix

In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better accuracy than the already proposed methods, while works for full and sparse matrices.     

关于布尔矩阵的广义Moore-Penrose逆

讨论布尔矩阵的广义Moore-Penrose逆.给出了一些广义Moore-Penrose逆存在的充要条件以及广义Moore-Penrose逆的一些刻划.     

整环上Moore-Penrose逆的刻画

若A为整环上的n阶可逆矩阵,则X=A-1是满足方程rank■=rank(A)的唯一矩阵.把它推广到满足Rao条件的整环上得到关于矩阵A的Moore-Penrose逆A+的刻画.     

三个矩阵乘积厄米特Moore-Penrose逆的等式与不等式

We investigate relationships between the Moore-Penrose inverse(ABA*)and the product [(AB)(1,2,3)]*B(AB)(1,2,3)through some rank and inertia formulas for the difference of(ABA*)-[(AB)(1,2,3)]*B(AB)(1,2,3),where B is Hermitian matrix and(AB)(1,2,3)is a {1,2,3}-inverse of AB.We show that there always exists an(AB)(1,2,3)such that(ABA*)= [(AB)(1,2,3)]*B(AB)(1,2,3)holds.In addition,we also establish necessary and sufficient conditions for the two inequalities(ABA*) [(AB)(1,2,3)]*B(AB)(1,2,3)and(ABA*)[(AB)(1,2,3)]*B(AB)(1,2,3)to hold in the L¨owner partial ordering.Some variations of the equalities and inequalities are also presented.In particular,some equalities and inequalities for the Moore-Penrose inverse of the sum A + B of two Hermitian matrices A and B are established.     

二元Boolean矩阵的加权Moore-Penrose逆

主要研究了二元Boolean矩阵A的加权Moore-Penrose逆的存在性问题,给出了二元Boolean矩阵A的加权Moore-Penrose逆存在的一些充分必要条件,并讨论了加权Moore-Penrose逆存在时的若干等价刻画及惟一性问题.     

矩阵moore—penrose逆的一种简捷求法

本文结出了利用AA~H或A~HA的特征多项式求矩阵A的moore-peuroxe逆的方法。     

关于Fuzzy矩阵的广义逆

本文分别给出了Fuzzy矩阵存在广义{1,3}-逆、广义{1,4}-逆以及Moore-Penrose广义逆Fuzzy矩阵的一些充要条件。又得到求上述广义逆Fuzzy矩阵的一些公式。主要的结果有: 1.Fuzzy矩阵A的广义{1,3}-逆A~((1.3))(广义{1,4}-逆A~((1.4))存在的充要条件是Fuzzy关系方程有解。2.Fuzzy矩阵A的Moore-Penrose广义逆A~T存在的充要条件是Fuzzy关系方程均有解。3.如果B、C分别为Fuzzy关系方程的一个解,那么。     

Additive Maps Preserving Moore-Penrose Inverses of Matrices on Symmetric Matrix Spaces

Suppose F is a field of characteristic not 2. Let M_nF and S_nF be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from S_nF to S_nF (respectively, M_nF) preserving Moore-Penrose inverses of matrices are characterized. We first characterize all additive Moore-Penrose inverse preserving maps from S_nF to M_nF, and thereby, all additive Moore-Penrose inverse preserving maps from S_nF to itself are characterized by restricting the range of these additive maps into the symmetric matrix space.