查询词典 diagonalizable matrix

At first, the paper quote a kind of special matrix ---sign symmetric matrix , anti sign symmetric matrix , weakly sign symmetric matrix and introduced some important results in spectral property about them from some bibliographies. And then, the paper extended the formerly results and gave more general conclusions about spectral property of sign symmetric matrix.

本文首先引入了一类特殊矩阵的概念——符号对称矩阵，反符号对称矩阵以及弱符号对称矩阵，在相关文献中对这类矩阵谱特征的已经有了一些结论，本文在前人研究的基础上将相关结论做了进一步的推广，得出了有关这类符号对称矩阵谱特征的更一般性的结论。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

In many practice problems such as to know the resonnance frequency of a structure and to know the critical value for the stability of a dynamical system,often need to compute the eigenvalues of a symmetric matrix. The chief method to compute the eigenvalues of a symmetric matrix is first to transformate the matrix to a symmetric tridiagonal matrix similarly and orthogonally, then to use the QR method with shift to the symmetric tridiagonal matrix.

很多实际问题，如求结构振动的固有频率，动力系统稳定性的临界值等常常归结为计算对称矩阵的特征值，而首选的计算方法是先把该矩阵正交相似变换成一个对称三对角矩阵，再对这个对称三对角矩阵用带位移的QR方法。1968年J.H。

Finally, a hospital viscosity of plasma diagnostic system is optimized by adjoint matrix method and M-P generalized inverse matrix method of MTS. The results show that adjoint matrix method can't select effective variables and M-P generalized inverse matrix method is robust.

最后，利用马氏田口伴随矩阵法和M-P广义逆矩阵法对某医院现阶段血粘度诊断系统进行优化，说明伴随矩阵法在选择有效变量时存在的问题和M-P广义逆矩阵法的稳健性。

The theory and approach are introduced, and the general expression containing arbitrary parameter is obtained for the feedback gain matrix. This method changes the problem of multi-input system to several problems of single-input. The number is the cycle index of system matrix. Compare with some known results, this method put forward that the least number of unknown entries of the feedback gain matrix is the order of the system matrix.

汽配置问题，得到了反馈增益矩阵的一般表达式，此表达式中含有任意参数，此方法将多输入线性系统极点配置问题转化为个数为系统矩阵循环指数的单输入系统的极点配置问题，进而推导出确定一个反馈增益矩阵的最少元素个数即为系统的阶数。

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖，其中‖·‖为Frobenius范数，S分别表示矩阵方程 AXB=D，AXA~T+BYB~T=D，AXB+CYD=E和矩阵方程组=，=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

The program is the main description of the matrix operations, including the basic matrix operations, matrix inverse, matrix singular value decomposition, and the characteristic value and characteristic vector solution and so on.

详细说明：该程序是主要描述的是矩阵运算，包括矩阵的基本运算，矩阵的求逆，矩阵的奇异值分解，以及特征值以及特征向量的求解等等。

When scaled factor circulant matrices are nonsingular, we can find the single solution of the scaled factor circulant matrix equation; When scaled factor circulant matrices are singular, we can find the special as well as the general solution of the scaled factor circulant matrix equation; There is only an error of approximation when the fast algorithm is implemented on computers, and only the elements in the first row of the scaled factor circulant matrix and the constants in the diagonal matrix are needed by the fast algorithm.

当鳞状因子循环矩阵非奇异时，该快速算法求出线性方程组的唯一解；当鳞状因子循环矩阵奇异时，该快速算法求出线性方程组的特解与通解。该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算。在计算机上实现时只有舍入误差。

Finite element method is used to build up element stiffness matrix and element mass matrix. After the combined total stiffness matrix and the total mass matrix are obtained.

采用有限元法建立不同管道元件的单元刚度矩阵和单元质量矩阵，最终形成管道结构的总刚度矩阵和总质量矩阵。

This dissertation puts forward a structuring method of some complicated problems as well as methods of combination of the judgment matrix on group decision basis demonstrates that these two ways strengthen the consistency of the judgment matrix. Besides, it makes some researches into theory of combination of judgment matrix on the group decision basis, suggests two methods of calculating the coefficient of the convex combination and puts forward a method to construct individual and comprehensive judgment matrix based on rough-set by cooperating with others accordingly.

5给出了群决策条件下复杂问题结构化方法；提出了群决策条件下群体AHP判断矩阵集结的两种方法，证明了这两种集结方法保持或改善了判断矩阵的一致性；研究了群决策条件下判断矩阵优化集结原理，给出了判断矩阵两种凸组合系数优化计算方法；合作提出了一个基于Rough Set的个体判断矩阵和综合判断矩阵构造方法。

I go to school at night.

我是上上学。

Clear Tip Nasal Aspirator: A soft time and gentle suction action makes removing excess mucus easy.

鼻吸明确提示：一个柔软的时间和温柔吸力行动使消除过剩的粘液容易。