逆的

The preface gave the definition and introduced history, background of development and significance of generalized inverse matrix.

前言从引进广义逆矩阵的定义着手，介绍了它的历史概况以及发展的背景及其意义；第1章从广义逆的发展历程讨论由Moor

Some formulas of the weighted Moore-Penrose generalized inverse of the sum of two matrices are given under two different kinds of conditions, related existing results are extend and modified with a sample and direct proof method.

在两种情形下，利用矩阵的加权Moore-Penrose逆导出了两矩阵和的加权Moore-Penrose逆的公式，其推导证明简洁而直接，文中还给出两矩阵可以同时加权奇异值分解的充要条件，指出了J.K。

In 1980 Cline and Greville gave the definition of the W-weighted Drazin inverse which is the extension of Drazin inverse.

Cline和Greville于1980年提出长方阵的加权Drazin逆的概念，它是方阵的Drazin逆的推广，有其实用背景。

In addition, we study the reduced minimum modulus of the generalized Drazin inverse of an operator on a Banach space and give out lower and upper bounds of the reduced minimum modulus of an operator and its generalized Drazin inverse, respectively.

第四章讨论了左乘算子L_A∈BB(H的约化极小模与A的约化极小模的关系；讨论了广义Drazin可逆算子的广义Drazin逆的约化极小模的上下界及广义Drazin可逆算子的广义Drazin逆的约化极小模与算子的约化极小模的关系。

Eliminating the restriction of the characteristic of field ,the forms of invertible linear operator preserving inverses of matrices over full matrix space with at least four elements are described.

去掉了域的特征限制，刻画了至少包含4个元素的任意域 F上的全矩阵空间Mn的保逆的可逆线性算子形式。利用保幂等的结论证明了f为Mn上保持逆矩阵的可逆线性算子当且仅当存在P∈GLn，使得f=εPAP-1，A∈Mn，ε=±1∈F；或者存在P∈GLn，使得f=εPATP-1，A∈Mn，ε=±1∈F

And then, this paper presents an algorithm of computing the left inverse or right inverse for these special rectangle matrices. In thenormal algorithms for solving these problems, we need O(m2n) multiplications ordivisions. The algorithms in this paper only need O + O(n2) multiplications ordivisions. The paper is built as follows.

常规的计算m×n阶不相容线性方程组的极小范数最小二乘解的算法所需计算量为O(m~2n)，而本文根据特殊矩阵的特殊结构，通过两种不同的构造方式给出了两类不同的计算极小范数最小二乘解的快速算法，并给出了求特殊矩阵的左逆及右逆的快速算法，它们的计算量均为O+O(n~2)。

In this paper, we shall apply this concept to the ring of linear operators on Banach space X and prove that if a linear operator T on a Banach space X is defined in all of X and has finite descent and ascent then there is a Drazin inverse T~D satisfying TT~DT~k=T~k, T~DTT~D= T~D, and T~DT=TT~D for some nonegative integer k.

以后又对方阵的Drazin逆作了深入的研究。它的一些性质可以参阅。同时对它的应用也作了许多研究，例如可以把Drazin逆的概念应用到Markov过程、线性微分方程组、差分方程组和最优控制等方面。

Estimation of parameters for general liner functional model with singular covariance. First, the Rao decomposition of the sample variance and the known singular measure error variance are presented and then the square measure error with singular variance and the standardized condition are got.

首先讨论了样本协方差与已知的奇异度量误差方差的Rao分解，给出了含有奇异方差广义逆的二次度量误差和模型的标准化条件，证明了二次度量误差与广义逆的选取无关。

On the one hand, the linear interpolation in plane makes it easy to separate the three-dimensional null subspace corresponding to rigid body motions, hence what is left to do is just to compute the inverse of a symmetric definite submatrix numerically.

在物理坐标系中的线性插值函数便于将三个刚体模式分离出来，从而只需计算对称正定子阵的逆，避免了求广义逆的数值困难；在参考坐标系中的高阶插值函数则可保持原平面弹性单元的列式方式。

2If the generalized inverses of Me exists, give the matix representations of it?

2若Mc的广义逆存在，它的广义逆的矩阵表示形式是怎样的？

Methods: Five patients with parkinsonism or dystonia were assigned to general anesthesia using an modified endotracheal tube.

本实验依照人体实验之相关规定进行，五位患有帕金森氏症或肌张力异常的病人接受神经立体定位手术。

If you can benefit from this book, it is our honour.

如果您能从本书获益，这将是我们的荣幸。