homogeneous linear equations

Some Properties of a Basic System of Solutions in a System of Homogeneous Linear Equations

齐次线性方程组的基础解系的一些性质

An Appliance on the Solution Theorem of System of Homogeneous Linear Equations

齐次线性方程组解理论的一个应用

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。

This article given another kind of proof using algebra method by system of homogeneous linear equations to the geometry question .

本文对这一几何问题利用齐次线性方程组给予了代数方法的又一种证明。

With the help of auxiliary variables or plane , a graphical solution for homogeneous linear equations is presented .

借助于辅助变量，或辅助平面，提出了齐次线性方程组的图解法。

The principle of the necessary and sufficient condition applied of the system of homogeneous linear equations is applied in this paper for the solution of some problems in elementary mathematics .

用齐线性方程组有非零解的充要条件定理解决初等数学中的某些问题。

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。

By solving a set of low order homogeneous linear equations to obtain a optimum stimulus , and by checking the screened branches in the nominal network excited by this optimum stimulus , the faulty branches can be located .

通过求解一组低阶齐次线性方程而得到一组最优激励，检查标称网络在最优激励下的被屏蔽支路集，即可对故障定位。

By use of Hopfield model and basis solution of homogeneous linear equations which are established in accordance with consistent state , a practical decision method for the existence of optimal Hopfield model of combinational circuits is provided . Finally , several examples are given .

采用组合电路Hopfield模型，通过相容状态建立的齐次线性方程组的基础解系，提出了组合电路最优Hopfield模型存在性的实用判定方法，并给出了计算实例。

Column Action Method for Fundamental System of Solutions of Homogeneous of Linear Equations

齐次线性方程组基础解系列处理法

The Properties of Solutions of Non homogeneous Linear Differential Equations with Small Growth

慢增长系数非齐次微分方程解的性质

A General Proof of Reduced Order Theorem for System of Homogeneous Linear Differential Equations

齐线性微分方程组降阶定理的一个一般证明

Subnormal Solutions of Second Order Homogeneous Linear Differential Equations with Periodic Coefficients

周期系数二阶齐次线性微分方程的次正规解

Distance between Adjacent Zero Point of Solution for the Third Order Homogeneous Linear Differential Equations

三阶线性齐次微分方程解的相邻零点之间的距离

A formula to solve initial value problem of homogeneous linear differential equations with constant coefficients and its application

常系数齐次线性微分方程组初值问题的求解公式及其应用

Much discussion has been made on the methods for the solution to homogeneous linear difference equations with constant coefficients , but none are simple enough .

常系数齐次线性差分方程组的求解方法，已有作者讨论过，但都没有给出一个比较简便的计算方法。

A new solution to the system of homogeneous linear differential equations and the system of homogeneous linear difference equations with constant coefficients is given . An interesting relation between the two systems is discussed .

给出了求解常系数线性齐次微分方程组和常系数线性齐次差分方程组的一个方法，指出了这两种方程组之间存在的一个有趣关系。

Then , we discuss several types of k-order non-homogeneous linear difference equations with constant coefficients . According to the character of the equations , we transfer them to higher order homogeneous linear difference equations .

其次，我们讨论了几类k阶常系数非齐次线性差分方程，根据非线性项的特征，将其化为更高阶齐次线性差分方程。

In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients .

本文利用张量分析给出了常系数线性常微分方程组和n阶常系数线性常微分方程初值问题一般解的显式表示，包括特征根有重根时的情况。

By the representation of general solutions of the higher order homogeneous linear difference equations , we obtain a special solution of the original non-homogeneous linear difference equation , and then the general solutions of the non-homogeneous linear difference equation are obtained .

通过相应高阶齐次线性差分方程的通解形式，获得其特解的简单表达形式，从而获得非齐次线性差分方程通解形式。

Using the Elementary Line Transformation of Matrix Extract the Normal Orthogonal System of Solution of Homogeneous Linear System of Equations

用矩阵的初等行变换求齐次线性方程组的标准正交解系

Undetermined coefficient method and its proof for non homogeneous linear ordinary difference equations are systematically given .

从三个方面，系统地给出了二阶常系数线性非齐次差分方程的待定系数解法及其证明。

This note presents a method to solve a homogeneous system of linear equations by giving linear independent vectors as a system of basic solutions .

给出求以已知一组线性无关的向量为基础解系的齐次线性方程组的方法。

The method of undetermined coeffcients used to find the first integral of a system of homogeneous linear ordinary differential equations with constant coefficents

求常系数线性齐次微分方程组初积分的待定系数法

In this paper a method is put forward to extract the normal orthogonal system of solution of homogeneous linear system of equations using the elementary line transformation of matrix .

提出一个用矩阵的初等变换求线性方程组的解空间的标准正交基的方法。

This paper discusses the further characteristic of the homogeneous system of linear equations solution space , as well as the application in the proof of matrix rank equality .

讨论齐次线性方程组解空间的进一步性质，以及在矩阵秩等式证明中的应用。

The global conformality condition can be regarded as a homogeneous algebraic system of linear equations with the unknowns of the smoothing cofactors , and its solutions form a prime module over R [ x , y ] .

整体协调条件可以看作一个以各内网线上光滑余因子为未知数的有着多项式系数的代数方程组，而这个代数方程组的所有解构成了多项式环R[x，y]上的素模。

In this paper , the sufficient and necessary conditions of row ( column ) full rank matrix and the row ( column ) full rank solution to homogeneous matrix equation are obtained . It also discusses the matrix decomposition and its application in the theory of homogeneous linear equations

本文建立了行（列）满秩矩阵和齐次矩阵方程有行（列）满秩解的充要条件，并讨论了矩阵分解及其在齐次线性方程组的应用