After solving the system of linear algebraic equations, another problem is induced that requires revising this coefficient matrix in order to get a new system of equations.
在线性代数方程组已解出之后，另一个课题需要修改它的系数矩阵，从而得到一个新的方程组。
To the inverse problem of the system of linear algebraic equations, tiauthor gives a symmetric matrix solution and the expression of its general solution.
本文给出线性代数方程组反问题的对称矩阵解，及其通解表达式。
The method ICCG. is one of the best iterative method for solving the system of linear algebraic equations, but it can only be applied to the symmetric and positive definite coefficient matrix.
ICCG方法是解线性代数方程组较为理想的方法，但它仅适用于具有正定对称的系数阵。
In this paper, a parallel iterative algorithm for linear equations is given by approximating inverse of a matrix.
文章利用近似逆矩阵构造了一类求解线性方程组的并行迭代算法。
Several properties about matrix with consistent perturbation are studied and applied into linear equations.
研究了矩阵列(行)一致扰动的几个性质，并应用于线性方程组。
This paper presents directly the general solution to sets of linear equations by properly bordering on augmented matrix and elementary transformation, and produeces some theoretical proving.
通过对增广矩阵适当“加边”，利用矩阵的初等行变换，直接求出线性方程组的通解形式，并在理论上给予了论证。
In this paper, an algorithm for finding the inverse matrix of tridiagonal matrix by solving systems of linear algebraic equations is proposed.
根据三对角矩阵的特点，给出一种利用解线性方程组的方法求三对角矩阵的逆矩阵的算法。
On the base of a variety of calculation of matrix used on the empowering bipartite graph, the solutions are further given to solve the linear equations in the graphs.
本文在赋权二部图上施行矩阵的各种运算之基础上，进一步给出用图求解线性方程组的方法。
Row standard simplest form matrix is introduced, the traditional solution of system of linear equations is improved and the solution process is standardized.
本文引进规范行最简形矩阵概念，改进了线性方程组的传统解法，并规范了解题过程。
The article discusses rank of a matrix by the solution theorem of system of homogeneous linear equations, and proves several famous inequalities and two propositions on rank of a matrix.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The judging methods of the vectors group related dependence from determinant values, rank of matrix, solution of system of linear equations etc were studied.
将行列式的值、矩阵的秩、齐次线性方程组的解等知识运用于向量组线性相关性判定，归纳出六种判定向量组线性相关性的方法。
The red and black ordering method about the coefficient matrix of a class of linear equations and the condition number of schur complement matrix deduced from red and black matrix are studied.
研究了一类线性方程组系数矩阵的红黑排序方法，以及由红黑排序矩阵导出的舒尔补矩阵的条件数。
This paper deals with the system of linear equations with matrix variables and gives the sufficient and necessary condition of consistency.
本文讨论以矩阵为变量的线性方程组，给出相容性的充要条件。
Based universal Grey number's characteristic, universal Grey matrix is defined and universal Grey matrix Solution Method to universal Grey Linear Equations is introduced.
根据泛灰数的性质，定义了泛灰矩阵，提出了泛灰线性方程组的泛灰矩阵解法，并给出了算例。
The inverse problems are researched on linear transformation, system of linear equations, diagonalizing of matrix, and so on.
本文就线性代数中几个重要知识点：线性变换、线性方程组的解、矩阵对角化等的逆向问题进行研究。
Linear equations of sparse matrix are solved by Biconjugate Gradients Stabilized Method and nonlinear algebraic equations are solved by parameter-regulated iterative procedures.
稳定化双共轭梯度法用于求解稀疏线性方程组，可调节参数的修正迭代法用于求解非线性代数方程组。
The feasibility and convergence of the BIMV method are proved when the coefficient matrix a of interval linear equations is an interval H-matrix.
当区间线性方程组的系数矩阵a为区间H阵时，证明了BIMV算法的可行性与收敛性。
Large sparse system of linear equations are solved by sparse matrix methods.
利用稀疏矩阵技术求解大型稀疏线性方程组。
Then, the learning of the weight matrix can be done by means of solving a group of systems of linear equations. Last, the mathematical base of the outer-product leaming method is pointed out.
将权矩阵的学习过程归结为用梯度下降法求一组矛盾线性方程组的过程；
In general situation, the coefficient matrix of linear equations deduced by the Boundary Element Method (BEM) is a compact one.
一般情况下，边界元法所建立的线性方程组系数矩阵为一满置矩阵。
The old methods about solving a system of linear equations all base on using the row's elementary operation to matrix of coefficients or augmented matrix.
现有的关于线性方程组的解法，都是基于对系数阵或增广阵施行初等“行”变换。
Several properties about matrix with consistent perturbation are studied and applied into linear equations. Error bounds with the solution perturbation are given.
研究了矩阵列（行）一致扰动的几个性质，并应用于线性方程组。给出了线性方程组系数矩阵一致扰动下解的相对误差界。
The name of it comes from the lower-triangular form of system matrix in state-space equations when it is linear.
这一名称来源于下三角结构线性系统写成状态空间表达式后，系统矩阵中所表现出的下三角形状；
A state transfer matrix differential equation was derived from the three-dimensional equilibrium equations and constitutive equations of a homogeneous, isotropic linear elastic body.
本文从三维弹性力学最基本的平衡方程和本构关系出发，推导出状态传递微分方程。
A transfer matrix differential equation is derived from the three-dimensional equilibrium equations and constitutive equations of a homogeneous, isotropic linear elastic body.
从三维弹性力学最基本的平衡方程和本构关系出发，推导出状态传递微分方程。
From the point view of applications, the matrix element of the involved linear system of equations is an explicit expression without numerical integration.
从应用角度看就是最终线性方程组每一元素均为显式表达，没有数值积分。
This paper discussed a new solution to homogeneous linear equations, hiding basic solutions in a matrix.
本文讨论用矩阵的初等变换求得基础解系的另一种方法，使基础解系隐含在一个矩阵之中。
The article gives the reversible condition of a kind of jump Vandermonde matrix through linear equations, and recursion formula and the expression of its inverse Matrix.
在一元数值积分公式的基础上，提出了二重数值积分的复合公式，并给出复化复合公式和逐次减半的复合递推公式，通过实验比较了两种算法。
Homogeneous linear equations of n-variables have the non-zero solutions when the rank of its matrix is less than n.
在线性方程组有解判别定理的基础上，给出了一个判定非齐次线性方程组存在全非零解的方法。
Homogeneous linear equations of n-variables have the non-zero solutions when the rank of its matrix is less than n.
在线性方程组有解判别定理的基础上，给出了一个判定非齐次线性方程组存在全非零解的方法。
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