普通的矩阵广义逆研究由来已久也趋于成熟。
Research on matrix generalized inverses is of long standing and tends to be mature.
先得到计算矩阵的广义逆的一种有效算法，即正交反向传播（OBP）算法，利用OBP 算法，经有限次迭代即可以得到矩阵广义逆的精确解。
We first get an effective algorithm for generalized inversion of a matrix, i. e. OBP algorithm. The exact generalized inversion of a matrix is obtained after finite steps by using OBP algorithm.
利用广义逆矩阵并构造辅助系统 ，将降价观测器的存在条件转化为判断辅助系统的可镇定性 。
The existence condition is then transformed to the stabilizability of the assistant system through a generalized inverse matrix and the assistant system.
这里，广义逆矩阵和去耦的电力系统灵敏度矩阵得到了广泛的应用。
In this paper, generalized inverse matrix and decoupled sensitivity matrix of power system are widely used.
摘要讨论了分块矩阵的广义逆，以及用矩阵的满秩子块表示广义逆。
The generalized inverse of partitioned matrices and the expression of generalized inverse using maximal nonsingular submatrix are discussed.
用矩阵的奇异值分解和广义逆讨论标准线性规划问题解的存在性和唯一性问题。
Apply singular value decomposition and generalize inverse of the matrix to discuss the existence and uniqueness of the solution of the standard linear programming problem.
利用广义逆矩阵的理论，本文给出了完整的最小二乘递推算法，并由此得到若干很有意义的推论。
Using the theory of generalized inverse matrix, a perfect algorithm of recurrence for least square has been derived. And from this algorithm, some corollaries of great significance were obtained.
本文叙述了加权广义逆矩阵的概念。
The concept of weighted generalized inverse matrices is described in this paper.
引入了广义逆矩阵，提出了一个新的算法。
The generalized inverse technique of matrix is introduced, and a new algorithm is developed.
近年来，矩阵的加权广义逆成了矩阵理论研究的热点，许多学者在这个领域做出了一定的成果，我们也得到了一些有意义的结论。
Recent years, the weighted generalized inverses of matrices become a research hotspot of matrix theory. Many authors made some achievements in this field. We also got some interesting results.
讨论了L-非负定矩阵的广义B-D逆的代数扰动问题，并给出了它的代数扰动表达式。
In this paper, the algebraic perturbation theory of generalized B-D Inverse of L-nonnegative definite matrix is discussed. and the expressions of the algebraic perturbation are presented.
在结构设计、振动系统、自动控制、矩阵对策等领域中存在各种各样的矩阵逆特征值问题及广义逆特征值问题。
There are all kinds of inverse eigenvalue and generalized inverse eigenvalue problems in the fields of structural design, vibration system, automation control and matrix decision etc.
即利用矩阵分析理论中的广义逆法，完成非线性方程组的最小二乘求解过程。
The paper also proposes the relevant numerical solver. Namely, it has Solved the equations uses the generalized reciprocal method in the theory of matrix analysis.
讨论了当矩阵A为满秩矩阵时求其广义逆的一种方法，并将此方法推广，给出当A为非满秩矩阵时求其广义逆的一般方法，同时给出算例。
This paper discusses the way about how to get the reflexive general inverse matrix of a full rank matrix A, and generalize this way, gives the general way for not full rank matrix.
给出了四元数矩阵加权广义逆的表达式，回答了关于四元数矩阵加权（3，4）和（2，4）逆表达式的公开问题。
The expression of the weighted generalized inverse of quaternion matrices are expressed, and the open question on the characterization of the (3,4) and (2,4) inverse are solved.
利用广义逆矩阵理论，将观测器的参数设计问题转化为求解一个参数矩阵的问题上来。
Then the design of the unknown matrices of the functional observer is converted to the design of a parameter matrix using the theory of generalized inverse.
讨论了一般符号模式矩阵的幂等性和广义逆。
I discuss idempotent, generalized inverses of general sign pattern matrix.
广义逆力法是一种以力法为力学概念基础，以广义逆矩阵理论为数学理论基础，以迭代求解为求解方式的新算法。
Generalized inverse matrix (GIM) is a new force method based on the generalized inverse matrix theory, which is an iteration method for solving material nonlinear problems.
但计算逆矩阵和岭脊的选择是广义岭估计的两个难点。
It is difficult to compute inverse matrix and select ridges.
我们试对矩阵的广义初等变换作简要阐述并举例说明其在行列式求值、矩阵求逆及矩阵秩的有关证明等方面的应用。
We've studied that the wide-sense elementary transformation of a matrix, and illustrated its application in determinant calculation, matrix inversion and the rank of a matrix.
本文利用结构柔度矩阵与刚度矩阵之间的广义逆关系，建立了一种基于柔度的结构损伤定位方法。
According to the pseudo-inverse relationship between global stiffness matrix and flexibility matrix, a flexibility-based method for structural damage localization is presented.
本文主要研究有关矩阵的加权广义逆，加权极分解和矩阵偏序等方面的问题。
In this thesis, we mainly study problems on weighted generalized inverses, weighted polar decomposition, and partial orderings of matrices.
利用广义逆矩阵的特性，改进了线性约束梯度投影法的理论。
In this paper, the theory of gradient projection methods for linearly constrained optimization formerly fomulated by the author is further improved.
然后讨论了推广的循环矩阵，即准循环矩阵和广义循环矩阵，利用类似方法，也给出了它们的求逆阵和求行列式的方法。
The generalization of a theorem for circular matrix is given by using generalized Vandermonde matrix, and several properties of generalized circular matrix are obtained.
两种方法都可以利用广义逆矩阵求得显式解，具有可逆性、可交换性、结合性等优点，提高了曲面形状修改的效率和可控性。
Both methods can be solved explicitly by a pseudo-inverse matrix and are of invertible, commutative, and associative properties, which enhance the efficiency and controllability of the manipulation.
两种方法都可以利用广义逆矩阵求得显式解，具有可逆性、可交换性、结合性等优点，提高了曲面形状修改的效率和可控性。
Both methods can be solved explicitly by a pseudo-inverse matrix and are of invertible, commutative, and associative properties, which enhance the efficiency and controllability of the manipulation.
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